# Number theory

### 15-S3-Q5

Proof by contradiction, irrationality of square root 2, rational, C1.

[STEP III 2015 Question 5 (Pure)]

### 15-S1-Q8

Sum, divisibility, series, proof, C1.

[STEP I 2015 Question 8 (Pure)]

### 14-S1-Q1

Difference of squares, odd, even, C1.

[STEP I 2014 Question 1 (Pure)]

### 13-S3-Q5

Coprime, powers of prime, rational, C1.

[STEP III 2013 Question 5 (Pure)]

### 13-S2-Q7

Integer solutions to equations, prime, C1.

[STEP II 2013 Question 7 (Pure)]

### 11-S3-Q2

Polynomial, common factor, irrational, nth root, cubic equations.

[STEP III 2011 Question 2 (Pure)]

### 11-S2-Q2

Perfect squres, cubes, solution to equations, C1.

[STEP II 2011 Question 2 (Pure)]

### 11-S1-Q8

Cubes and squares, inequality, integer solution to equations, C1.

[STEP I 2011 Question 8 (Pure)]

### 10-S1-Q8

Divisibility, integer solution to equations, C1.

[STEP I 2010 Question 8 (Pure)]

### 09-S1-Q1

Proper factor, integer, prime factors, C1.

[STEP I 2009 Question 1 (Pure)]

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP