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15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Helen's Conjecture
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Age 11 to 14 Challenge Level:
Investigate
$$ 1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$$
and
$$ 2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$$
for different values of $n$.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.