Question

If $m,n\in \Bbb N$ s.t $m<n$ and the last three digits of $(2978)^m$ and $(2978)^n$ are same, what are the least value of $m$ and $n$?

score 514 · Answer 1 · 2020-07-01 07:14:07

If $m,n\in \Bbb N$ s.t $m<n$ and the last three digits of $(2978)^m$ and $(2978)^n$ are same, what are the least value of $m$ and $n$?

score 176 · Answer 2 · 2026-02-23 04:37:09

176

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List Question

If $m,n\in \Bbb N$ s.t $m<n$ and the last three digits of $(2978)^m$ and $(2978)^n$ are same, what are the least value of $m$ and $n$?

Deriving $KE=0.5mv^2$ from the relativity equation

Binomial theorem and logarithms

Double summation transition from Vandermonde's identity

Square a combinatorial formula (binomial theorem)

Multi-binomial theorem and double product expansion

Evaluate $\displaystyle\sum_{r=0}^8 (-1)^r \binom{20}{r} \binom{20}{8-r}$

Show that $\int_{0}^x \frac{1}{1+t^4} dt = x - x^5/5 + x^9/9 ..... $ where $\lvert x\rvert$ < 1

If $n \in \mathbb N$, find $\sum(-1)^r \binom{n}{r}\left(\frac {1} {2^r}+\frac {3^r} {2^{2r}}+\frac {7^r} {2^{3r}} + \cdots \text{m terms}\right)$

A finite sum closely related to the binomial series

Representing $n!$ as a Polynomial

Binomial Expansion Of $\frac{24}{(x-4)(x+3)}$

Proof appears to use substitution inconsistently.

Proving combinatorial identities

There is a binomial theorem. How about trinomial theorem?

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