1. If 30 in base b is 56 in base 12, find b?

2. Who first proved that prime numbers are infinitely many?

Solution

1. Answer: 22

Solution: (6 x 1) + (5 x 12) = 3b and so b = 22. 

2. Answer: Euclid of Alexandria, proved by a ingenious way that prime numbers are infinitely many. This proof by Euclid is considered as one among the best proofs in mathematics even today.