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3
Q 3
Q 3
Source:
May 25, 2007
Polynomials
Problem Statement
Let
n
≥
2
n \ge 2
n
≥
2
be an integer. Prove that if
k
2
+
k
+
n
k^2 + k + n
k
2
+
k
+
n
is prime for all integers
k
k
k
such that
0
≤
k
≤
n
3
0 \leq k \leq \sqrt{\frac{n}{3}}
0
≤
k
≤
3
n
, then
k
2
+
k
+
n
k^2 +k + n
k
2
+
k
+
n
is prime for all integers
k
k
k
such that
0
≤
k
≤
n
−
2
0 \leq k \leq n - 2
0
≤
k
≤
n
−
2
.
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