Number Theory
Quadratic Diophantine Equations
Magician Mike Michael claims to know two positive whole numbers that multiply to 1000, neither of which contain the digit 0.
What is the sum of these 2 numbers?
by
raghul krishnan
\[\large a!b! = a! + b! \]
If \(a\) and \(b\) are positive integers that satisfy the equation above, find \(a + b\).
by
Nihar Mahajan
If we mistakenly add numerator and denominators, we would think:
\[\Large \dfrac{1}{a} + \dfrac{1}{b}=\dfrac{2}{a+b}.\]
How many ordered pairs \((a.b)\) in the interval \(-10\leq a,b \leq 10\) such that they satisfy the equation above.
by
Nihar Mahajan
What is the smallest positive multiple of hundred which can be expressed as the product of two consecutive integers?
by
Ansh Bhatt
How many primes are 4 less than a perfect square?
by
Evan Glori