Question

Demonstrați că $18^{64}-1 \; \vdots \; 17$

Answer 1

Folosind formula:
$a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+...+ab^{n-2}+b^{n-1})$
avem:

$18^{64}-1=(18-1)(..................)\vdots17$