Question

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

Answer 1

117649

Explanation:

First lets evaluate the parts:

7^8 = 5764801

7^7 = 823543

7^6 = 117649

adding and subtracting these 3 values as stated in the expression results in 5058907 which when divided by 43 is 117649.

While there is probably a faster way to do this, this does work.