A number theory problem by Swadesh Rath

Number Theory Level 2

if 3y -1 = x^2 find no. of ordered Integral solutions of the equation


The answer is 0.

Swadesh Rath by Swadesh Rath , 25, India

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2 solutions

Curtis Clement
Aug 3, 2015

Lets consider the remainder left when both sides are divided by 3: L H S = 3 y − 1 ≡ − 1 ≡ 2 m o d ( 3 ) \ LHS= 3y -1 \equiv -1 \equiv 2 mod(3) R H S = x 2 ≡ 0 , 1 m o d ( 3 ) \ RHS = x^2 \equiv 0,1 mod(3) ∴ L H S ≠ R H S ( n o s o l u t i o n s ) \therefore\ LHS \ne RHS \ (no \ solutions)

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Swadesh Rath
Aug 8, 2015

3y - 1 = x^2 this is not possible because any square is of the form 3k or 3k+1 ... so no solutions.,

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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