In 1946, an American numerologist, Prof. W, predicted the downfall of the USA in the year 2141 based on what he called a profound mathematical discovery depending on the following expression:
1492^n - 1770^n - 1863^n + 2141^n
He spent many months calculating the value of this for n = 1, 2, 3 and so on up to 1945 and found the remarkable fact that the result was always divisible by 1946. Since the years 1492, 1770 and 1863 are all important in American history, he claimed that 2141 would also be significant - hence his prediction.
Show how he could have saved himself months of work.

my friend also sent me this:

((x^n)-(y^n)) = (x-y)(x^(n-1)+....+y^(n-1))