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Grosman Mathematical Olympiad
2023 Grosman Mathematical Olympiad
4
4
Part of
2023 Grosman Mathematical Olympiad
Problems
(1)
All values of a quadratic are semiprime
Source: 2023 Grosman MO, P4
9/8/2023
Let
q
q
q
be an odd prime number. Prove that it is impossible for all
(
q
−
1
)
(q-1)
(
q
−
1
)
numbers
1
2
+
1
+
q
,
2
2
+
2
+
q
,
…
,
(
q
−
1
)
2
+
(
q
−
1
)
+
q
1^2+1+q, 2^2+2+q, \dots, (q-1)^2+(q-1)+q
1
2
+
1
+
q
,
2
2
+
2
+
q
,
…
,
(
q
−
1
)
2
+
(
q
−
1
)
+
q
to be products of two primes (not necessarily distinct).
quadratics
number theory
prime numbers