Question

Prove the divisibility of the following numbers:

Problem A: 8^10−8^9−8^8 by 55 = ? * 55

Problem B: 81^7−27^9−9^13 by 45 = ? *45

Answer 1

$8^{10}-8^9-8^8=8^8(8^2-8-1)=8^8(55)$

$81^7-27^9-9^{13}=3^{28}-3^{27}-3^{26}=3^{26}(3^2-3-1)=3^{26}(5)=3^{24}(45)$