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Mathematics
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user3472
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9
Determinant of matrix with $2$'s and the pattern $3\ 1\ 3$
Nov 8, 2021
8
Prove that $\Phi_{420}(69) > \Phi_{69}(420)$
Nov 7, 2023
8
recurrence involving permutations
Dec 1, 2021
8
prove that $\int_0^\infty \frac{\sin^2 x-x\sin x}{x^3} \, dx= \frac{1}{2} - \ln 2$
Nov 14, 2021
7
compute the integral $\int_0^1 \int_0^1 \int_0^1 \frac{1}{(1+x^2+y^2+z^2)^2} dxdydz$ [duplicate]
Oct 20, 2021
6
Prove that $\frac{1}{a_1} + \cdots + \frac{1}{a_n} = 1$ implies $a_n < 2^{n!}$ [duplicate]
Apr 9, 2022
6
Prove that $a_{n+1} = a_n^2 - a_n+1$ for all $n$ large enough
Jun 9, 2022
6
there are infinitely many numbers $n$ so that $2^n$ ends in $n$
Nov 25, 2021
6
Prove that $\lim_{x\to 0^+} 1/x^a \int_0^x t^{a-1} f(t) dt$ exists if and only if $\lim_{x\to 0^+} 1/x^b \int_0^x t^{b-1} f(t) dt$
Oct 18, 2023
5
Prove that for all integers $a,b, b\neq 0,$ there exists $n$ with $v_2(n!) \equiv a\mod b$.
Oct 18, 2023