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Which triangular numbers are also squares?

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#elementary-number-theory #diophantine-equations #square-numbers #pell-type-equations
165
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Triangular numbers for numbers.

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#number-theory #diophantine-equations
393
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The sum of two triangular numbers.

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#number-theory #diophantine-equations
79
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Find two triangles of longest side length 25?

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#diophantine-equations
147
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The equation $b^2=a(a^2-1)$ has no rational solutions except obvious ones

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#number-theory #diophantine-equations #elliptic-curves
251
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Find the generating function for a series , given a recurrence relation

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#discrete-mathematics #recurrence-relations #diophantine-equations
178
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How find this $x^3-5x+10=2^y$

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#number-theory #diophantine-equations
517
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diophantine equation $ |x^2-py^2|=\frac{p-1}{2} $

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#number-theory #elementary-number-theory #prime-numbers #diophantine-equations
112
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Solve a system of diophantine equations

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#number-theory #elementary-number-theory #diophantine-equations #divisibility
100
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Solving diophatine equation of form $x^2+y^2=25$

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#elementary-number-theory #diophantine-equations
1.2k
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integer solutions to $x^2+y^2+z^2+t^2 = w^2$

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#number-theory #diophantine-equations #sums-of-squares
1k
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Positive integer solutions to $x^2+y^2+x+y+1=xyz$

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#number-theory #elementary-number-theory #diophantine-equations #vieta-jumping
227
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When is the sum of consecutive squares a prime?

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#algebra-precalculus #elementary-number-theory #prime-numbers #diophantine-equations #sums-of-squares
346
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Find all integer solutions of $x^4 + 2x^3 + 2x^2 + 2x +5 = y^2$

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#number-theory #polynomials #diophantine-equations
1.8k
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Any simpler proof of Catalan's conjecture?

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#number-theory #diophantine-equations

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