Number Theory

Quadratic Diophantine Equations

Quadratic Diophantine Equations: Level 2 Challenges

         

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?

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Raghul Krishnan by raghul krishnan

a!b!=a!+b!\large a!b! = a! + b!

If aa and bb are positive integers that satisfy the equation above, find a+ba + b.

Nihar Mahajan by Nihar Mahajan

If we mistakenly add numerator and denominators, we would think:

1a+1b=2a+b.\Large \dfrac{1}{a} + \dfrac{1}{b}=\dfrac{2}{a+b}.

How many ordered pairs (a.b)(a.b) in the interval −10≤a,b≤10-10\leq a,b \leq 10 such that they satisfy the equation above.

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Nihar Mahajan by Nihar Mahajan

What is the smallest positive multiple of hundred which can be expressed as the product of two consecutive integers?

Ansh Bhatt by Ansh Bhatt

How many primes are 4 less than a perfect square?

Evan Glori by Evan Glori
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