Math Challenges: Find Pairs, Units Digit, Perfect Squares, Last Digit

[guss]

1. Find the number of pairs (m, n) such that 2^m - 2ⁿ = 63 in which m and n are nonnegative integers.

2. What is the units digit of 6²⁵ - 3²⁴ ?

3. How many perfect squares divide the number 4!*5!*6! ?

4. What is the last digit of the sum 1! + 2! + 3! + ... + 2010! + 2011! ?

Thanks!

 

[gsal]

it does not quite work like that...you need to show some genuine effort of what you have tried and show us where you are stuck, etc.

 

[guss]

Yeah, sorry, never mind. I got them solved.