mathlove

 130 Mental Calculations 79 How to prove that the Fibonacci sequence is periodic mod 5 without using induction? 54 Trick with 3-digit numbers, always get 1089 45 Which of the following powers is bigger: $2^{41}$ or $3^{24}$? 43 Are Mersenne prime exponents always odd?

### Reputation (92,888)

 +15 Showing that two numbers are the same percent different from their average. +5 $12345679$ and friends +100 Primality test for numbers of the form $N=4 \cdot 3^n+1$ +10 Combinatorics problem about listing numbers $1,2,…n$

### Questions (180)

 84 Numbers $n$ such that the digit sum of $n^2$ is a square 69 Representing every positive rational number in the form of $(a^n+b^n)/(c^n+d^n)$ 54 Finding triplets $(a,b,c)$ such that $\sqrt{abc}\in\mathbb N$ divides $(a-1)(b-1)(c-1)$ 53 Arranging numbers from $1$ to $n$ such that the sum of every two adjacent numbers is a perfect power 47 Why does this ratio of sums of square roots equal $1+\sqrt2+\sqrt{4+2\sqrt2}=\cot\frac\pi{16}$ for any natural number $n$?

### Tags (294)

 1k algebra-precalculus × 427 360 trigonometry × 183 756 calculus × 319 360 limits × 128 727 elementary-number-theory × 226 346 sequences-and-series × 148 501 geometry × 293 316 number-theory × 190 436 inequality × 180 305 summation × 100

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 Mathematics 92,888 rep 883220 MathOverflow 1,904 rep 11243