Celebrating 10000 points
Number Theory
Level
3
m=n^2-n
a is greatest number that always divides m^2-2m for n,m are always integers
find total no. of possible factors of a^2[excluding 1 and itself]
The answer is 19.
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1 solution
m^2-2m=[n-2][n-1][n][n+1]
divisible by 4!
a=24
a^2=576=2^6*3^2 total factors=[6+1][2+1]=21
but exclude 1 and 576
so,there are 19 such factors