A number theory problem by Ferdinand Halim Santoso

Number Theory Level 3

Find the number of integers x x such that 12 x 3 + 8 x 2 + 4 x + 2 12x^3 + 8x^2 + 4x + 2 is a perfect square .


The answer is 0.

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Ferdinand Halim Santoso by Ferdinand Halim Santoso , 18, Indonesia

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1 solution

We know if 12 x 3 + 8 x 2 + 4 x + 2 = 2 m o d 4 12x^3+8x^2+4x+2=2 mod 4 And we know there aren't perfect square that congruent 2 mod 4 So there aren't integer x

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