SOLUTION: How do i show for integers m and n and a natural number k that is greator and equal to 1. m divides n right arrow m divides n^(k).

Question 26242: How do i show for integers m and n and a natural number k that is greator and equal to 1.
m divides n right arrow m divides n^(k).
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
How do i show for integers m and n and a natural number k that is greator and equal to 1.
m divides n right arrow m divides n^(k).
M|N........HENCE....N=M*A ...WHERE A IS AN INTEGER
TPT....M|N^K
K IS AN INTEGER GREATER THAN EQUAL TO ONE .HENCE N^K=N*N*N.....K TIMES
HENCE N^K DIVIDED BY M = N*N*N...K TIMES/M=A*N*N*....(K-1)....
SINCE A,N ARE INTEGERS AND (K-1) IS ALSO AN INTEGER GREATER THAN ZERO WE PROVED THAT N^K/M IS AN INTEGER. HENCE M|N^K

RELATED QUESTIONS
Suppose that a and d are integers. m and n are natural numbers such that d divides... (answered by richard1234)

Define a relation R on the set of integers by mRn if and only if 3 divides m - n. Prove (answered by jim_thompson5910)

Conjecture: Find all positive integers 'a' such that there exists an integer 'm' with the (answered by richard1234)

Conditional proof M->(K->L) (L\/N) -> J Therefore, M-> (K->J) That's supposed to be (answered by math_helper)

For arbitrary positive integers k, m, and n, will there exist a prime p such that... (answered by Edwin McCravy)

Let (Fn)=(1,1,2,3,5,8,13,21,34,55,...) be the fibonacci sequence defined by F1=F2=1,... (answered by venugopalramana)

Suppose that m and n are opposite integers with m > n. If a = m^2 - n^2, b = 2mn, and c = (answered by ikleyn)

The function f(n) takes the integers to the real numbers such that f(m + n) + f(m - n) = (answered by CPhill,ikleyn)

If f is a function such that for all integers m and n, f(m,1) = m+1 and f(m,n) =... (answered by MathLover1)