Question

Prove that 38^3+37^3 is divisible by 75

Answer 1

my first guess would be to factor

Answer 2

\[a^3+b^3=(a+b)(a^2-ab+b^2)\] try it with \(a=38,b=37\)

Answer 3

(38+37)(38^2-38*37+37^2)

Answer 4

And (38+37) = 75, thus it is divisible by 75

Q.E.D.