You can put this solution on YOUR website! prove by mathematical induction that x-y is a factor of x^n- y^n
1.test for n=1....(X^1-Y^1)=X-Y.IS DIVISIBLE BY (X-Y)
2.ASSUME IT IS TRUE FOR N=K
SO (X^K-Y^K) IS DIVISIBLE BY (X-Y)...LET X^K-Y^K=A(X-Y)...WHERE A IS AN INTEGER.
3.T.S.T FOR X=K+1....THE STATEMENT IS TRUE
X^(K+1)-Y^(K+1)=X^(K+1)-Y^(K+1)+X^K-Y^K-(X^K-Y^K)=X^K(X+1)-Y^K(Y+1)-(X^K-Y^K)
=(X^K-Y^K)(X+1-Y-1)-(X^K-Y^K)=(X^K-Y^K)(X-Y)-(X^K-Y^K)=AN INTEGER SINCE EVERY TERM IS DIVISIBLE BY X-Y...
SO IT S TRUE FOR X=K+1
4.BUT THIS IS TRUE FOR X=1..SO IT IS TRUE FOR 1+1=2...2+1=3....ETC..FOR ALL INTEGRAL VALUES OF N
