Irrationality, proof by contradiction, C1.

[STEP I 2008 Question 1 (Pure)]

Balanced number, sum of digits, C1.

[STEP I 2007 Question 1 (Pure)]

Perfect square, inequality, factors, C1.

[STEP I 2006 Question 1 (Pure)]

Euler totient function, prime factors, proof, counterexample, C1.

[STEP II 2005 Question 2 (Pure)]

Sum of digits, C1.

[STEP I 2005 Question 1 (Pure)]

Arithmetic progression, square, solution, C1.

[STEP I 2004 Question 5 (Pure)]

Inequality, divisibility, sum of digits, C1.

[STEP I 2003 Question 7 (Pure)]

Divisibility, average value, C1.

[STEP I 1999 Question 1 (Pure)]

Cubic equation, factors, integer solution to equation, C1.

[STEP II 1998 Question 1 (Pure)]

Sum of numbers, digits, product of primes, C1.

[STEP II 1997 Question 1 (Pure)]