Super Perfect Squares

Number Theory Level 5

a 2 + 1 = 2 b 4 \large a^2 + 1 = 2b^4

Given that a a and b b are positive integers satisfying the equation above, what is the largest possible value of a a ?


The answer is 239.

Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

Kazem Sepehrinia
Sep 18, 2016

By Ljunggren’s theorem the only solutions to this equation are ( a , b ) = ( ± 1 , ± 1 ) , ( ± 239 , ± 13 ) . (a, b)=(\pm1, \pm1), ( \pm 239, \pm13).

1 Helpful 0 Interesting 0 Brilliant 0 Confused

For those who don't know what this is, I think this is what Mr. Sepehrinia is talking about.

Chaebum Sheen - 4 years, 9 months ago

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Exactly. Though I came across this after reading about Pell's equation.

Worranat Pakornrat - 4 years, 9 months ago

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