Question

find the number which always divides (49 power 15 -1)

Answer 1

Consider below geometric sum :
$1+49+49^2+\cdots+49^{14}=\dfrac{49^{15}-1}{49-1}$
$\implies~(49-1)(1+49+49^2+\cdots+49^{14})=49^{15}-1$

Therefore, $49-1=48$ divides $49^{15}-1$

Answer 2

Consider below geometric sum :

1+49+49^2+\cdots+49^{14}=\dfrac{49^{15}-1}{49-1}

\implies~(49-1)(1+49+49^2+\cdots+49^{14})=49^{15}-1

Therefore, 49-1=48 divides 49^{15}-1

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