A perfect square number

Level 2

Given an integer x x such that 4 x + 1 4x+1 is a perfect square number.

What is the condition of x x to achieve the above?

Product of 2 consecutive even numbers. Any value of x x works Product of 2 consecutive numbers A multiple of 10. No value of x x works. Any odd value works. Sum of 2 consecutive numbers Sum of 2 consecutive odd numbers.

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1 solution

For x=a(a+1), 4x+1=4a(a+1)+1=4 a 2 a^2 +4a+1= ( 2 a + 1 ) 2 (2a+1)^2 , which is a perfect square.

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