MathDB

1

Part of 2019 India Regional Mathematical Olympiad

Problems(2)

Rationally yours!

Source: RMO 2019 P1

10/20/2019
Suppose xx is a non zero real number such that both x5x^5 and 20x+19x20x+\frac{19}{x} are rational numbers. Prove that xx is a rational number.
RMOalgebrarational numbers
Sum of gcd of n and 2019-n.

Source: RMO maharashtra and goa 2019 P1

11/10/2019
For each n∈Nn\in\mathbb{N} let dnd_n denote the gcd of nn and (2019−n)(2019-n). Find value of d1+d2+⋯d2018+d2019d_1+d_2+\cdots d_{2018}+d_{2019}
number theorygreatest common divisor