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Does the equation $a^2 + b^2 + c^2 = d^2$ have solutions in integers if $(a, b, c, d) > 0$?

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#proof-verification #sums-of-squares #perfect-squares
81
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Permutation such that the sum of a number and its position is a square

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#sequences-and-series #perfect-squares
163
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What must the value of $y$ be so that $a$ and $b$ are integers?

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#proof-verification #conjectures #pythagorean-triples #perfect-squares
1.2k
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Perfect Squares: relatively prime and increasing arithmetic progression

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#number-theory #elementary-number-theory #perfect-squares
111
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Determine when $(3^x - y^3)(x^3 - 3^y)$ is a perfect square

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#elementary-number-theory #perfect-squares
807
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Prove $n! +5$ is not a perfect square for $n\in\mathbb{N}$

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#number-theory #elementary-number-theory #square-numbers #perfect-squares
5k
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Sum of digits of perfect square

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#number-theory #elementary-number-theory #square-numbers #perfect-squares
721
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$(a^2+b^2-ab)(a^2+b^2-2ab)$ is a perfect square

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#number-theory #elementary-number-theory #arithmetic #diophantine-equations #perfect-squares
229
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Number of odd perfect squares,n, in the interval 1-a inclusive

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#number-theory #elementary-number-theory #perfect-squares
135
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Finding multipliers to create nearly perfect squares

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#elementary-number-theory #continued-fractions #square-numbers #perfect-squares
135
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On the square values of a certain polynomial

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#elementary-number-theory #polynomials #diophantine-equations #perfect-squares
70
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Method for pefect square

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#elementary-number-theory #perfect-squares
145
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Prove that there exist no natural number k such that $3^k+5^k$ is a square of an integer number?

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#elementary-number-theory #divisibility #square-numbers #provability #perfect-squares
758
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Polynomial that is a square in every positive integer

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#polynomials #perfect-squares
713
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Prove that every terms of a sequence defined by a recurrence relation is a perfect square.

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#sequences-and-series #number-theory #recurrence-relations #perfect-squares

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