A number theory problem by Mohit Musaddi

Number Theory Level pending

How many triples $(a,b,c)$ of positive integers satisfy $2^{a} -5^{b}*7^{c} =1?$

infinite 1 0 2

1 solution

Patrick Corn
Aug 24, 2014

If $5|(2^a-1)$ , then $4|a$ (look mod 5), but then $2^a-1$ is divisible by $2^4-1 = 3 \cdot 5$ , so then $2^a-1 = 5^b 7^c$ is impossible since there is no $3$ on the right side.

A number theory problem by Mohit Musaddi

1 solution

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