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Ede207 Assignment 17

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Introduction

This STEP support module includes some work with summations, and an introduction to Modular Arithmetic. Previous assignments can be found here, but you can do this one without having done the others first.

STEP questions are difficult, they are supposed to be and you should expect to get stuck. However, as you tackle more and more STEP questions you will develop a range of problem solving skills (and spend less time "being stuck"). Support is available on the STEP Support discussion forum.

About this assignment

The assignment is published as a pdf file below. Each STEP Support assignment module starts with a warm-up exercise, followed by preparatory work leading to a STEP question. Finally, there is a warm-down exercise.

The warm up for this assignment introduces Modular Arithmetic and shows how you can use this to find divisibility tests for dividing by 3 and 11.

The main STEP question (2003 STEP I Question 1) derives the results for the sum of $n$ squares and $n$ cubes.

The final question is about using modulo arithmetic to prove that expressions are divisible by certain numbers (these sorts of questions are more usually presented as exercises in proof by induction, but using modulo arithmetic can often be a simpler approach).

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