Powers of 2

A #Number #Theory gem based on #PigeonHole principle.

Prove that there exist two powers of 2 which differ by a multiple of 2020.

#PrimeMaths #Integers #Divisibility

More Problems for Practice:

Problem 1. Prove that of any 52 integers, two can always be found such that the difference of their squares is divisible by 100.

Problem 2. 15 boys gathered 100 nuts. Prove that some pair of buys gathered an identical number of nuts.

Problem 3. Given 11 different natural numbers, none greater than 20. Prove that two of these can be chosen, on of which divides the other.

Problem based on Angle bisector

If AD is the angle bisector of ∠BAC in the triangle ABC. Show that AB.AC=BD.DC+AD^2.

#Solution https://t.me/PrimeMaths/43

#Geometry #PrimeMaths #Angle #Bisectors