Showing what's behind the curtain

Counting the number of consecutive nines at the beginning of the fractional part of (√p+√q)^{2n}

Find the continued fractions for N ≤ 10000 have an odd period.

Investigate the Diophantine equation *x*^{2} − D*y*^{2} = 1.

Find the number of fractions that lie between 1/3 and 1/2 in a sorted set of reduced proper fractions.

How many elements would be contained in the set of reduced proper fractions for d ≤ 1,000,000?

Listing reduced proper fractions in ascending order of size.

Find the value of d < 1000 for which 1/d contains the longest recurring cycle.

Discover all the fractions with an unorthodox cancelling method.