Showing what's behind the curtain

Find how many Pythagorean triangles allow tiling with a perimeter < 100,000,000.

Determining the value of infinite polynomial series for which the coefficients are Fibonacci numbers.

Investigating isosceles triangle for which the height and base length differ by one.

Finding the maximum remainder when (a ā 1)^{n} + (a + 1)^{n} is divided by a^{2}.

Finding square sums that are palindromic.

Investigating which primes will never divide a repunit containing 10**n digits.

Determining the first forty prime factors of a very large repunit.

Finding composite values, n, for which nā1 is divisible by the length of the smallest repunits that divide it.

Investigating minimal repunits that divide by n.

Count how many numbers below a googol (10**100) are not “bouncy”