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## 'Iff' printed from http://nrich.maths.org/

Take some triangular numbers. Multiply each one by eight and add
one.There is an interesting pattern - can you spot it? Test your
conjecture with some other triangular numbers.

Can you prove that the pattern continues for any triangular
number?

If you are finding it tricky to
construct a proof, an activity is available here which allows you to put a proof we have
written in the correct order. Alternatively, look at the hint for a
visual way of thinking about this problem.