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jgsmath
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5 Questions

Score Activity Newest Views
11 votes
2 answers
1k views

If 25 divides $a^5 + b^5 + c^5 + d^5 + e^5$ then prove that 5 divides $abcde$.

elementary-number-theory
asked Jun 17, 2017 at 22:27
10 votes
3 answers
914 views

Birthday Paradox with Leap Year

probability solution-verification birthday
asked Jan 29, 2021 at 16:00
5 votes
1 answer
122 views

Let $n$ be any positive integer and let $x \in (0, \pi)$. Prove that $\sin x+ \frac{\sin 3x}{3} + \cdots +\frac{\sin(2n-1)x}{2n-1}$ is positive. [duplicate]

calculus real-analysis
asked Jun 14, 2017 at 23:03
3 votes
2 answers
164 views

Prove that $(k^3)!$ is divisible by $(k!)^{k^2 + k + 1}$. Proof using properties of greatest integer function?

elementary-number-theory proof-verification contest-math
asked Jul 3, 2017 at 20:47
2 votes
1 answer
235 views

Let $m,n \in \mathbb{Z}^+$ and $f(m,n) = 36^m - 5^n$. When is $\min |f(m,n)|$ attained?

elementary-number-theory
asked Jun 18, 2017 at 3:31
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