Tutors Answer Your Questions about Divisibility and Prime Numbers (FREE)
Question 2634: a cook cuts a cake into 35 equal pieces and an identical cake into 42 pieces. The caterer, however, insists that the cakes be cut exactly alike. Into how many pieces must each cake now be cut
Click here to see answer by khwang(438)  |
Question 4388: I am having a lot of trouble with these proofs; I get so far and alskdjfl....
prove or give a counterexample: if a and b are integers such that 6 divides both a+b and a-b, then 3 divides both a and b.
Show that the third power of every integer that is not divisible by 7 is of the form 7k+1 or 7k-1 where k is an integer.
Prove: if n is an integer, then one of the integers n, n+2, and n+4 is divisible by 3. Use it to show that n=3 is the only integer such that n, n+2, and n+4 are primes.
Prove or give a counterexample: if d=(a,b), then 3d=(3a,3b)
Prove or give a counterexample: if a and b are integers such that a^2 divides b^3, then a divides b.
Prove or give a counterexample: if the product of two integers is divisible by 3, then at least one of the integers is divisible by 3.
Click here to see answer by khwang(438) |
Question 6222: Use the binomial theorem and mathematical induction to show the following. Let p be a prime. Then for any integer a, we have a^p =a (mod p). The "=" sign should be congruence. I need help, I have no idea what they want.
Click here to see answer by khwang(438) |
Question 10288: I have created a method that tests divisibility by 7 and 13.
It reduces an integer (doesn't matter its extension) to a two-digit number. Original number and reduced number divided by 7 will leave the same remainder.
I would like to have your opinion about my method that is available at the site: www.7and13divisibility.com
My best regards
Silvio Moura Velho
Click here to see answer by longjonsilver(2297)  |
Question 10808: is 1^5+2^5+3^5+.....+100^5 congruent to 0(mod 4).
i know that all even numbers in this problem are divisible by 4. my problem lie in the odd numbers since some of them has a remainder 1 and some 3.is there a pattern for these odd numbers to know how many of them has a remainder 1 and how many has a remainder 3.
Click here to see answer by khwang(438) |
Question 12138: Hello-
I need,(in a 6th grade defintion),help on DIVISIBILTY, and PRIME AND COMPOSITE NUMBERS!! It would help If you could explain the rules for:
2,5,10,and,3. and If possible type a short list of PRIME NUMBERS, and, COMPOSITE NUMBERS!! >.< My teacher didn't explain this in an eaasy way...LOL!!
The worksheet is divided into four boxes, and in each box, I need to find all the numbers divisible by: 2,5,10,3. In each box I need to color in the numbers to create a picture!! THIS IS SO CUNFUSING!!!!
NEED HELP ASAP!!!!
Sincerely,
-Anonymous
Click here to see answer by rapaljer(4667)  |
Question 12319: How do u prove this?...Show that 3 divides n^3-n for all positive integers n. And does 4 divide n^4-n for all positive intgers n? AND i need to use proof by induction i think, i get the first part but then get stuck at the end...please help
Click here to see answer by khwang(438) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440
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