Lesson The number which gives remainder 4 when divided by 7, remainder 5 when divided by 8 and remainder 6 when divided by 9

Source code of 'The number which gives remainder 4 when divided by 7, remainder 5 when divided by 8 and remainder 6 when divided by 9'

This Lesson (The number which gives remainder 4 when divided by 7, remainder 5 when divided by 8 and remainder 6 when divided by 9) was created by by ikleyn(52781)

: View Source, Show
About ikleyn:

<H2>The number which gives remainder 4 when divided by 7, remainder 5 when divided by 8 and remainder 6 when divided by 9</H2>

<H3>Problem 1</H3>Find the least positive integer number satisfying each of the following conditions :
&nbsp;&nbsp;&nbsp;&nbsp;- Divided by &nbsp;7 &nbsp;gives a remainder of &nbsp;4.
&nbsp;&nbsp;&nbsp;&nbsp;- Divided by &nbsp;8 &nbsp;gives a remainder of &nbsp;5.
&nbsp;&nbsp;&nbsp;&nbsp;- Divided by &nbsp;9 &nbsp;gives a remainder of &nbsp;6.

<B>Solution</B>

<pre>
Let N be that number.

Consider the number N+3.

Then it is divisible by 7; by 8 and by 9 with no remainder.

So the number  N+3  is a multiple of the product 7, 8 and 9:  N+3 = 7*8*9 = 504.

Hence,  N = 504-3 = 501.    <U>ANSWER</U>
</pre>

My other lessons in this site on miscellaneous problems on divisibility of integer numbers are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Light-flashes-on-a-Christmas-tree-and--a-Least-Common-Multiple.lesson>Light flashes on a Christmas tree and a Least Common Multiple</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/The-number-that-leaves-a-remainder-1-when-divided-by-2-by-3-by-4-by-5-and-so-on-until-9.lesson>The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/Introductory-problems-on-divisibility-numbers.lesson>Introductory problems on divisibility of integer numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Finding-Greatest-Common-Divisor-of-integer-numbers.lesson>Finding Greatest Common Divisor of integer numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/Relativity-prime-numbers-help-to-solve-the-problem.lesson>Relatively prime numbers help to solve the problem</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Solving-equations-in-integer-numbers.lesson>Solving equations in integer numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Quadratic-polynomial-with-odd-integer-coefs-can-not-have-a-rational-root.lesson>Quadratic polynomial with odd integer coefficients can not have a rational root</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/Proving-the-equation-has-no-integer-solutions.lesson>Proving an equation has no integer solutions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Composite-number-of-the-form-%284n%2B3%29-must--have-a-prime-divisor-of-the-form-%284n%2B3%29.lesson>Composite number of the form (4n+3) must have a prime divisor of the form (4n+3)</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Problems-on-divisors-of-a-given-number.lesson>Problems on divisors of a given number</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/How-many-three-digit-numbers-are-multiples-of-both-5-and-7.lesson>How many three-digit numbers are multiples of both 5 and 7?</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/How-many-3-digit-numbers-are-not-dvsbl-by-2-not-dvsbl-by-3-notdvsbl-by-either-2-or-3.lesson>How many 3-digit numbers are not divisible by 2; not divisible by 3; not divisible by either 2 or 3</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/How-many-integer-numbers-in-the-range-1-300-are-divisible-by.lesson>How many integer numbers in the range 1-300 are divisible by at least one of the integers 4, 6 and 15 ?</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Find-the-remainder-of-division.lesson>Find the remainder of division </A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Why-3%5En%2B7%5En-2-is-divisible-by-8-for-all-positive-integer-n.lesson>Why 3^n + 7^n - 2 is divisible by 8 for all positive integer n ?</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/What-is--the-last-digit-of-the-number-a%5En.lesson>What is the last digit of the number a^n ?</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Find-the-last-three-digits-of-these-numbers.lesson>Find the last three digits of these numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Find-the-two-last-digits-of-the-number-3%5E123%2B7%5E123%2B9%5E123.lesson>Find the last two digits of the number 3^123 + 7^123 + 9^123</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/Find-the-last-two-digits-of-%281%21-%2B-2%21-%2B-3%21-%2B-%2B-2024%21%29%5E2024.lesson>Find the last two digits of (1! + 2! + 3! + ... + 2024!)^2024</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Find-n-th-term-of-a-sequence.lesson>Find n-th term of a sequence</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Solving-one-Diofantine-equation.lesson>Solving Diophantine equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Determine-the-number-of-integer-solutions-to-equation-n%5E2%2B18n%2B3=m%5E2.lesson>How many integers of the form n^2 + 18n + 13 are perfect squares</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Miscellaneous-problems-on-divisibility-numbers.lesson>Miscellaneous problems on divisibility numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Two-digit-numbers-with-digit-9.lesson>Two-digit numbers with digit "9"</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Find-the-sum-of-digits-of-integer-numbers.lesson>Find the sum of digits of integer numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Find-a-triangle-with-integer-side-lengths-and-integer-area.lesson>Find a triangle with integer side lengths and integer area</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Math-circle-level-problem-on-the-hundred-handed-monster-Briareus.lesson>Math circle level problem on the hundred-handed monster Briareus</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Math-Citcle-level-problem-on-lockers-and-divisors.lesson>Math Circle level problem on lockers and divisors of integer numbers</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Nice-entertaiment-problem-What-numbers-John-is-thinking-about.lesson>Nice entertainment problems related to divisibility property</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Solving-problems-on-modular-arithmetic.lesson>Solving problems on modular arithmetic</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/Using-the-little-Fermat-theorem-to-solve-a-problem-on-modular-arithmetic.lesson#google_vignette>Using the little Fermat's theorem to solve a problem on modular arithmetic</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/divisibility/lessons/OVERVIEW-of-miscellanious-solved-problems-on-divisibility-of-numbers.lesson>OVERVIEW of miscellaneous solved problems on divisibility of integer numbers</A>