Tagged Questions
2
votes
5answers
115 views
$x^2\mid27 \implies x\mid9$ : Prove
$x$ is given as a natural number.
I was trying this by direct proof: assume $27\mid x^2$, then $x^2 = 27m \Longrightarrow x=3\cdot \sqrt{3m} \Longrightarrow \sqrt{3m}$ must be integer ...
3
votes
0answers
235 views
Proof that $ 1^3+2^3+\cdots +n^3 = (1+2+\cdots+n)^2$ without using induction [duplicate]
Possible Duplicate:
Intuitive explanation for the identity $\sum\limits_{k=1}^n {k^3} = \left(\sum\limits_{k=1}^n k\right)^2$
How to prove this without using mathematical induction?
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3
votes
3answers
135 views
If $n\equiv 2\pmod 3$, then $7\mid 2^n+3$.
In this (btw, nice) answer to Twin primes of form $2^n+3$ and $2^n+5$, it was said that:
If $n\equiv 2\pmod 3$, then $7\mid 2^n+3$?
I'm not familiar with these kind of calculations, so I'd like ...
