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When will an arithmetic progression contain a square number?

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#number-theory #square-numbers #arithmetic-progressions
269
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Prove that every integer greater than 1 is sum of square and squarefree.

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#number-theory #elementary-number-theory #analytic-number-theory #square-numbers #sieve-theory
1.4k
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Perfect square product among 17 integers

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#combinatorics #discrete-mathematics #elementary-set-theory #pigeonhole-principle #square-numbers
520
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Second digit of square numbers in binary yields $\sqrt2$

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#sequences-and-series #elementary-number-theory #binary #number-systems #square-numbers
20
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Finding solution of a set of equations such that the results are perfect squares.

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#polynomials #systems-of-equations #square-numbers
180
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Are there infinite many squares with a decimal expansion having no consecutive equal digits?

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#number-theory #decimal-expansion #square-numbers
450
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Sum of exactly n perfect square divisors

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#elementary-number-theory #prime-numbers #prime-factorization #square-numbers
129
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Is there an infinite number of numbers like $1600$?

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#number-theory #recreational-mathematics #square-numbers #sums-of-squares #experimental-mathematics
706
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What is the relation between the perfect squares and prime numbers?

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#probability #number-theory #prime-numbers #square-numbers
159
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Can this be continued forever?

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#elementary-number-theory #recreational-mathematics #square-numbers #sums-of-squares #experimental-mathematics
78
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Not sure how to find out what $x$ is...

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#algebra-precalculus #square-numbers #cubics
634
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For a primitive pythagorean triple $(a, b, c)$, prove $(c+b), (c-b)$ are both squares.

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#elementary-number-theory #prime-factorization #square-numbers #pythagorean-triples
931
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If N is a quadratic residue modulo p for all primes p<N, is N a perfect square?

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#number-theory #square-numbers #quadratic-residues
283
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Product of 2-digit numbers

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#elementary-number-theory #recreational-mathematics #puzzle #square-numbers
266
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How to get a perfect square with this condition?

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#square-numbers

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