Questions Asked

ganeshie8:
Group Title
For the year 2015, determine the following:
a) the calendar dates on which Mondays will occur in March.
b) the months in which the 13th will…
 updated 4 days ago
 209 replies
 13 Medals

ganeshie8:
Group Title
3f(x2) + f(2x) = 5x
f(x) = ?
…
 updated 7 days ago
 56 replies
 9 Medals

ganeshie8:
Group Title
Find all integers \(n\) that satisfy the equation
\[(n1)^3 + n^3 + (n+1)^3 = (n+2)^3\]
…
 updated 7 days ago
 13 replies
 7 Medals

ganeshie8:
Group Title
how this interesting pattern works ?
1 * 9 + 2 = 11
12 * 9 + 3 = 111
…
 updated 10 days ago
 55 replies
 10 Medals

ganeshie8:
Group Title
show that \(a^n+b^n=c^n\) has no solutions in prime numbers for all integers \(n \gt 2\)
…
 updated 12 days ago
 54 replies
 4 Medals

ganeshie8:
Group Title
Easy yet interesting problem !
Show that \(n^{15}+1\) is composite for all integers \(n\ge 2\)
 updated 12 days ago
 23 replies
 9 Medals

ganeshie8:
Group Title
find the maximum value of \[25(ab)^2 + (\sqrt{1004a^2}+5\sqrt{1b^2})^2\]
 updated 15 days ago
 83 replies
 9 Medals

ganeshie8:
Group Title
find the integer solutions of \(px^2 + 2 = y^2\) where \(p\) is an odd prime
 updated 17 days ago
 75 replies
 6 Medals

ganeshie8:
Group Title
numbers of form \( 1111111\ldots \)
 updated 18 days ago
 109 replies
 9 Medals

ganeshie8:
Group Title
show that \(\large (p1)!^{p} + 1\) is divisible by \(\large p^2\)
\(p\) is an odd prime
 updated 19 days ago
 58 replies
 4 Medals

ganeshie8:
Group Title
looking for a simple proof
show that
…
 updated 21 days ago
 58 replies
 4 Medals

ganeshie8:
Group Title
Find any 3 consecutive integers such that each of them is divisible by a perfect square > 1
 updated 22 days ago
 50 replies
 5 Medals

ganeshie8:
Group Title
Write 375007 as a product of two primes. No calculators please.
 updated 22 days ago
 7 replies
 4 Medals

ganeshie8:
Group Title
\[\large \lim\limits_{x\to 0^{+}} \left[ x\left[\dfrac{1}{x}\right]\right] = ?\]
 updated 23 days ago
 41 replies
 6 Medals

ganeshie8:
Group Title
show that \(\large \frac{10^{12n6}1}{99} \) is not divisible by \(101\) for all \(n \in \mathbb{Z^{+}}\)
 updated 24 days ago
 92 replies
 9 Medals

ganeshie8:
Group Title
show that \[\large \int\limits_0^{\infty} \dfrac{x^{a}\,dx}{1+x^b} =
\frac{\pi}{b\sin(\pi(a+1)/b )}\]
…
 updated 25 days ago
 28 replies
 14 Medals

ganeshie8:
Group Title
Show that\[\large \int\limits_0^1 x^{2014}(1x)^{2015}\, dx = \dfrac{(2015!)^2}{2015[((2(2015))!]}\]
 updated 27 days ago
 23 replies
 6 Medals

ganeshie8:
Group Title
Evaluate \[\large \int \limits_0^{\infty}\frac{e^{x}}{\sqrt{x}} \, dx = \sqrt{\pi} \]
@Marki
 updated 27 days ago
 42 replies
 5 Medals

ganeshie8:
Group Title
Find the remainder when \( 4^{2015} + 5^{2015}\) is divided by \(9\)
 updated 28 days ago
 64 replies
 11 Medals

ganeshie8:
Group Title
Show that the number of coprime positive integers less than \(2^n1\) is divisible by \(n\) for all \(n\gt 1\)
 updated one month ago
 68 replies
 4 Medals

ganeshie8:
Group Title
Factor \((111111)_2\) in binary
 updated one month ago
 82 replies
 6 Medals

ganeshie8:
Group Title
Challenge problem : Show that \(F(a) = \frac{2^{2^{a+1}}1}{2^{2^a}+1}\) is an integer for all \(a \in \mathbb{N} \)
 updated one month ago
 21 replies
 13 Medals

ganeshie8:
Group Title
Find one prime divisor of \(2^{5903}1\)
 updated one month ago
 118 replies
 10 Medals

ganeshie8:
Group Title
\(f(x) = x^2 + \pi x + 1\) and \(\alpha, \beta\) are zeroes of \(f(x)\) find the value of \((\alpha + 1)(\beta + 1)\)
 updated one month ago
 43 replies
 9 Medals

ganeshie8:
Group Title
prove \[\lim_{t\to0}\dfrac{f(x)^t1}{t}=\ln(f(x))\]
 updated one month ago
 26 replies
 6 Medals

ganeshie8:
Group Title
parameterize the closed surface obtained by rotating the region inside the
first quadrant enclosed by
y = x^3
…
 updated one month ago
 34 replies
 7 Medals

ganeshie8:
Group Title
Volumes of revolution
 updated one month ago
 169 replies
 6 Medals

ganeshie8:
Group Title
Is this function continuous? Justify
 updated 2 months ago
 34 replies
 9 Medals

ganeshie8:
Group Title
Evaluate \(\rm \int\limits_3^5 f^{1}(x) dx \) if \(\rm f(x) = x^5+x+3\)
 updated 2 months ago
 60 replies
 10 Medals

ganeshie8:
Group Title
summation by parts formula
 updated 2 months ago
 30 replies
 3 Medals
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