perplexus.info :: Just Math : Product 2 Power Not

Product 2 Power Not (Posted on 2008-07-12)

Prove that there does not exist any triplet (A, B, C) of positive integers, that satisfy this equation:

(36A + B)(36B + A) = 2^C

See The Solution Submitted by K Sengupta

Rating: 3.5000 (2 votes)

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And further ...

| Comment 3 of 6 |

Gamer's excellent proof also is easily extended to prove there does not exist any quadruplet (A,B,C,D) of positive integers such that

(2DA + B)(2DB + A) = 2^{C

In other words, there is nothing special about 36. Any positive even number works just as well.}

Edited on July 12, 2008, 11:22 pm

Posted by Steve Herman on 2008-07-12 22:44:21

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