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King's Maths School

Challenge 281: Two Thirteen Things

Can you track down any multiples of 13 in this challenge?

(i) Is 3k – 1 ever a multiple of 13? Justify your conclusions clearly, and if you think the answer is yes, state clearly all the the values of k for which this holds.

(ii) Is 3k + 1 ever a multiple of 13? Justify your conclusions clearly, and if you think the answer is yes, state clearly all the the values of k for which this holds.