Hawk

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bio website N/A location Kolkata, India age 20 member for 1 year, 1 month seen Nov 21 at 11:34 profile views 519

I am a beginner, highly interested in maths. I do not know much but have that special thing that helps one proceed, keen interest.

103 Questions

 50 Can 18 consecutive integers be separated into two groups,such that their product is equal? 25 Any natural number is greater than or equal to its product of digits. 11 Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square. 7 If a prime can be expressed as sum of square of two integers, then prove that the representation is unique. 7 If $\dfrac{a}{b-c}+\dfrac{b}{c-a}+\dfrac{c}{a-b}=0$ with unequal $a,b,c$, Prove that $\dfrac{a}{(b-c)^2}+\dfrac{b}{(c-a)^2}+\dfrac{c}{(a-b)^2}=0$

3,106 Reputation

 +5 Let $n$ be a positive integer. If $2+2\sqrt{28n^2+1}$ is an integer, then it is a perfect square. +5 Evaluate the improper integral +10 Pigeon Hole. 80 numbered balls -2 Locus of the centre of a circle $\Gamma$

 19 How to prove this inequality $x + \frac{1}{x} \geq 2$ 5 Find the value of $a^{2m}+a^m+{1\over a^m}+{1\over a^{2m}}$ 5 Find the number of ways in which $A,B,C,a,b,c$ can be arranged so that the capital letters occur before the small letters. 5 how do i prove that $\sin(\pi/4)=\cos(\pi/4)$? 4 Find a formula for $\sin(5x)$ in terms of $\sin(x)$ and $\cos(x)$.

71 Tags

 32 inequality × 24 6 elementary-number-theory × 40 15 algebra-precalculus × 26 6 calculus × 9 13 combinatorics × 22 6 discrete-mathematics × 5 10 number-theory × 4 5 pigeonhole-principle × 3 7 real-analysis × 16 5 pi

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