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Aug
23
comment Raising $2$ to the power of $2014^ {2013}$ modulo $41$
How do you calculate the last ?
Aug
23
comment Raising $2$ to the power of $2014^ {2013}$ modulo $41$
@Artemisia, Thta's why I reached at $20$. $a$ is an integer, right and $1^a=?$
Aug
23
answered Were exactly did I go wrong in rationalizing denominator?
Aug
23
comment Raising $2$ to the power of $2014^ {2013}$ modulo $41$
@Artemisia, My Pleasure. See also: math.stackexchange.com/questions/905906/…
Aug
23
comment Raising $2$ to the power of $2014^ {2013}$ modulo $41$
@Artemisia, You have hinted $$2^{10}\equiv-1\pmod{41}\implies2^{20}=(2^{10})^2\equiv?$$
Aug
23
answered Raising $2$ to the power of $2014^ {2013}$ modulo $41$
Aug
23
comment Trigonometric series problem: finding a second valid solution.
@user144533, math.stackexchange.com/questions/117114/…
Aug
23
comment modules with several powers $x^{y^z}$
@user1991779, We can apply Fermat, Euler Totient theorem etc. and make some calculations if $(a,m)=1$ that's why the division by gcd$(1001,42)$ .Also find $\#9$ of mathworld.wolfram.com/Congruence.html
Aug
23
comment If $y^{\frac{1}{m}} + y^{\frac{-1}{m}}=2x$, show that $x^2y_{n+2}+(2n+1)xy_{n+1} + (n^2-m^2)y=0$
@rsadhvika, $$\frac{d^n{y_2(x^2-1)}}{dx^n}=(x^2-1)\frac{d^n(y_n)}{dx^n}+\binom n1\frac{d(x^2-1)}{dx^1}\frac{d^{n-1}(y_n)}{dx^{n-1}}+\binom n2\frac{d^2(x^2-1)}{dx^2}\frac{d^{n-2}(y_n)}{dx^{n-2}}+0$$ as $$\frac{d^m(x^2-1)}{dx^m}=0$$ for $m\ge3$
Aug
23
comment If $y^{\frac{1}{m}} + y^{\frac{-1}{m}}=2x$, show that $x^2y_{n+2}+(2n+1)xy_{n+1} + (n^2-m^2)y=0$
@rsadhvika, See wdjoyner.com/teach/calc1-sage/html/node106.html or en.wikipedia.org/wiki/Product_rule#Higher_derivatives
Aug
23
answered If $y^{\frac{1}{m}} + y^{\frac{-1}{m}}=2x$, show that $x^2y_{n+2}+(2n+1)xy_{n+1} + (n^2-m^2)y=0$
Aug
23
answered Find two roots for $\cos 5x=a$
Aug
23
comment How find this $\frac{1}{x-y}+\frac{1}{y-z}+\frac{1}{x-z}$ minimum of the value
@user84413, I think that should be dictated by the $2$nd derivative test
Aug
22
answered Repeated differentiation of $\frac{1}{1+x^2}$
Aug
22
comment Number Theory - Proof by Induction
math.stackexchange.com/questions/755125/…
Aug
22
comment Showing that $\sum\limits_{k=2}^n {k\choose2} = {{n+1}\choose 3}$ for integers $n\geq 2$
Generalization : proofwiki.org/wiki/Rising_Sum_of_Binomial_Coefficients
Aug
22
revised Find the total number of real solutions
added 8 characters in body
Aug
22
answered Find the total number of real solutions
Aug
22
comment Find the total number of real solutions
$$5^x+4^x+2\sqrt{20^x}=(5^{\frac x2}+4^{\frac x2})^2$$
Aug
22
comment How find this $\frac{1}{x-y}+\frac{1}{y-z}+\frac{1}{x-z}$ minimum of the value
@ThomasAndrews, It should be $$a+b-c=0$$