MathDB

Let

n

be a positive integer. Let

s: \mathbb N \to \{1, \ldots, n\}

be a function such that

n

divides

m-s(m)

for all positive integers

m

. Let

a_0, a_1, a_2, \ldots

be a sequence such that

a_0=0

and

a_{k}=a_{k-1}+s(k) \text{ for all }k\ge 1.

Find all

n

for which this sequence contains all the residues modulo

(n+1)^2

.
Proposed by N.V. Tejaswi

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