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2d
revised For any positive integers $a$ and $b$, the number $(36a+b)(a+36b)$ can never be a power of $2$.
edited body
2d
answered For any positive integers $a$ and $b$, the number $(36a+b)(a+36b)$ can never be a power of $2$.
2d
comment For any positive integers $a$ and $b$, the number $(36a+b)(a+36b)$ can never be a power of $2$.
That answer is not correct. The initial $a$ and $b$ are by assumption positive integers. So $36a_n+b_n$ and its mate are $\ge 37$ during the process, and are powers of $2$, so of course they are not $2^0$.
2d
comment For any positive integers $a$ and $b$, the number $(36a+b)(a+36b)$ can never be a power of $2$.
Yes, nicely done!
2d
comment Probability: put 20 distinct balls randomly in 12 urns
You are using a sample space that is very hard to work with. The reason is that not all elements of your sample space are equally likely. It is far easier to assume the balls are distinct (that does not affect the probability, just put ID's in invisible ink on the balls). The best sample space has $12^{20}$ elements.
2d
revised Finding the value of an expression involving co-efficients in binomial expansion
added 197 characters in body
2d
answered Problem about proving fermat's little theorem
2d
answered Finding the value of an expression involving co-efficients in binomial expansion
2d
comment If $p>2$ is a prime number, Prove that $U(p^k) $ is cyclic
The usual proof, that goes back to Gauss, consits of the following steps. (i) if $a$ is a primitive root of $p$, and $a$ does not have order $p-1$ modulo $p^2$, then $a$ is a primitive root of $p^2$; (ii) otherwise, $a+p$ is a primitive root of $p^2$; (iii) if $a$ is a primitive root of $p^2$, then $a$ is a primitive root of $p^k$ for all $k\ge 2$. None of the steps is terribly long, but a detailed proof takes a while.
2d
comment Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
No problem, yes, exactly the same idea. So if upvoting is appropriate for one, it is appropriate for the other.
2d
comment What is the conditional mass function of $X$ given that $Y = i$?
The "solutions" if quoted correctly, are ridiculous. No dependence on $y$, and a probability that is equal to $3$.
2d
answered Proving $\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$
2d
comment Minimum value Of trigonometry expression
Not necessarily better, but the solutions by lab bhattacharjee and lemur are very nice. I prefer non-calculus arguments. No really good reason!
2d
comment The sum of two triangular numbers.
The number $x(x+1)$ is not necessarily a triangular number. Triangular numbers are of the shape $x(x+1)/2$.
2d
answered Minimum value Of trigonometry expression
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comment Minimum value of trigonometric functions
That's an entirely different problem than the one you asked. There is a non-calculus way, also a calculus way. Which one do you want? The calculus way involves differentiating, it is fairly mechanical. But if you want a full answer, you will need to ask a separate question: writing at length in comments is difficult.
2d
comment Why isn't the zero after the decimal in $0.01$ significant?
A very informal answer: $1$ cm has one significant digit. If we measure in metres, we get $0.01$. No added accuracy!
2d
comment What is the significance of limit and why is there always a difference between the value of x and the limiting value?
Of course $\frac{0}{0}$ is undefined. But in a huge number of applications, it is useful to know what $\frac{f(x)-f(a)}{x-a}$ approaches as $x$ approaches $a$.
2d
answered Minimum value of trigonometric functions
2d
comment Intuition for rules of rounding numbers
There is no reason to close it. It is a perfectly good question, and there may be an at length answer that gives you more information than the Wikipedia article linked to above.