Philip Gibbs
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Prove that none of $\{11, 111, 1111,\dots \}$ is the perfect square of an integer
20 votes

A square number can never end with two odd digits If it did it would have to be the square of an odd number $x = 10a+b$ where $b$ is odd. $x^2 = 100a^2 + 20ab + b^2$ so you just have to check for $x ...

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Greatest common divisor of $2 + 3i$ and $1-i$ in $\mathbb{Z}[i]$
Accepted answer
6 votes

I would solve this be looking at the modulus square of each number and taking the common divisor of that. in this case $|2+3i|^2 = 4+9=13$ and $|1-i|^2=1+1=2$ the modulus square of any common divisor ...

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Rational solutions of Pell's equation
3 votes

There is a simple and more general way to look at this problem that applies to finding rational points on any conic section with rational coefficients. i.e. any equation in the form $ax^2 + bxy + cy^2 ...

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Order of operations: Matrix product and hadamard product
Accepted answer
3 votes

There is probably no convention, and if there is it is not sufficiently well known to be unambiguous. Authors using such a mixture would either have to declare their convention or (better still) use ...

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How to prove this fundamental relationship $ b=\ell+n-1$?
2 votes

This is true for a connected planar circuit (usually called a graph). To prove it just think about what happens to the value of $l + n - b$ whenever you reduce the circuit by removing a branch or a ...

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