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
