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Mathematics
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Hawk
  • Member for 10 years, 8 months
  • Last seen more than 9 years ago
  • N/A
  • Kolkata, India
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I am a beginner, highly interested in maths. I do not know much but have that special thing that helps one proceed, keen interest.

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73
Can $18$ consecutive integers be separated into two groups such that their product is equal?
Jan 14, 2014
32
How to prove this inequality $ x + \frac{1}{x} \geq 2 $
Mar 9, 2014
30
Any natural number is greater than or equal to its product of digits.
Mar 14, 2014
16
Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$ [duplicate]
Feb 24, 2014
16
If a prime can be expressed as sum of square of two integers, then prove that the representation is unique.
Mar 20, 2014
14
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
Feb 4, 2014
13
If $n$ is a positive integer greater than 1 such that $3n+1$ is perfect square, then show that $n+1$ is the sum of three perfect squares.
Jan 10, 2014
10
Let $f(x)=ax^2+bx+c$ where $a,b,c$ are real numbers. Suppose $f(-1),f(0),f(1) \in [-1,1]$. Prove that $|f(x)|\le \frac{3}{2}$ for all $x \in [-1,1]$.
Apr 29, 2014
9
There are 100 people in a queue waiting to enter a hall. The hall has exactly 100 seats numbered from 1 to 100. The first person in the queue...
Feb 20, 2014
9
Suppose that $P(x)$ is a polynomial of degree $n$ such that $P(k)=\dfrac{k}{k+1}$ for $k=0,1,\ldots,n$. Find the value of $P(n+1)$
Jan 13, 2014
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This question was edited but not by me, though it shows that I edited it myself. I'm curious to know about it.
3
Should all the questions need to be asked in English? I saw a question which was not in English...