Today Puzzle #551
Puzzle No. 551 鈥� Thursday 22 August
Thousands of students across the country pick up their GCSE results today. Here is a proof question that has appeared in a recent Maths GCSE exam paper. When you square an odd number, it is always 1 more than a multiple of 4. For example, 5 squared is 25, which is 1 more than 24, which is a multiple of 4. Can you prove this is always the case?
Today’s #PuzzleForToday has been set by Bobby Seagull and fellow maths teacher Susan Okereke, who are both co-hosts of the Maths Appeal podcast.
Click here for the answer
Let 2n be an even number. So an odd number might be 2n + 1.
If we square 2n + 1, we get (2n + 1)^2 = (2n + 1)(2n + 1) = 4n^2 + 4n + 1
4n^2 + 4n is always a multiple of 4. Then the 1 left over means an odd number squared will be always be 1 more than a multiple of 4.
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