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Weekly Maths Challenge

Seven Day Maths

Challenge 185: Reasoner's Remarkable Rules

Dr Reasoner (see challenges 160 and 173) is very excited about her new ideas concerning prime numbers.

Her first claim is that if p is a prime number, it is always possible to find a whole number n such that np + 1 is a square number. Is she right? If so, can you prove it? If not, can you adapt her claim to make it true?

Her second claim is that for any odd number n, there is always a prime p so that np + 1 is a square number. Can you prove (or disprove) her claim?



Mathematics is a subject where you learn best by tackling problems. Every week, a new problem will be posted here for you to pit your wits against.

We invite you to have a go at solving it. If you get stuck, keep trying, and do go away and come back later – you will often find that you have a better idea on your second, third or even fourth attempt. If you have solved the problem, you can send your solutions to weeklymaths@kcl.ac.uk. You are welcome to either scan in written work, or to type your solutions. If you are emailing for the first time, please let us know what year you are currently in and what school you are at.

Past problems can be accessed below, and we welcome submissions of solutions for those too.

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Good luck! 


 

Past Challenges

Weekly Challenge 184

Weekly Challenge 183

Weekly Challenge 182

Weekly Challenge 181

Weekly Challenge 180

Weekly Challenge 179

Weekly Challenge 178

Weekly Challenge 177

Weekly Challenge 176

Weekly Challenge 175

Weekly Challenge 174

Weekly Challenge 173

Weekly Challenge 172

Weekly Challenge 171

Weekly Challenge 170

Weekly Challenge 169

Weekly Challenge 168

Weekly Challenge 167

Weekly Challenge 166

Weekly Challenge 165

Weekly Challenge 164

Weekly Challenge 163

Weekly Challenge 162

Weekly Challenge 161

Older Challenges

Problems 141-160

Problems 121-140

Problems 101-120

Problems 81-100

Problems 61-80

Problems 41-60

Problems 21-40

Problems 1-20

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