Math 130
posted by Enis .
Sum the first two odd numbers, then the first three, the first four, and so on. From these observations could you guess the sum of the first 100 odd numbers?

1+3=4
1+3+5=9
1+3+5+7=16
notice it goes like this:
first two = 2^2
first three=3^3
first four= 4^2
first 15=15^2
first hundred= ??? 
How many fourdigit numbers abcd exist such that a is even, b is divisible by 5, c is prime, and d is odd?

Find the smallest values for a and b so that 21 base a equals 25 base b.