MathDB

2

Part of 2019 Auckland Mathematical Olympiad

Problems(2)

any 2 of 2109 segments intersect (2019 Auckland MO J2)

Source:

11/14/2021
There are 20192019 segments [a1,b1][a_1, b_1], ......, [a2019,b2019][a_{2019}, b_{2019}] on the line. It is known that any two of them intersect. Prove that they all have a point in common.
geometrysegments
exist a,b among 43 pos. integers 100 divides a^2-b^2 (2019 Auckland MO S2)

Source:

11/15/2021
Prove that among any 4343 positive integers there exist two aa and bb such that a2−b2a^2 - b^2 is divisible by 100100.
number theorydivisibledivides