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Moldova Team Selection Test
1995 Moldova Team Selection Test
2
2
Part of
1995 Moldova Team Selection Test
Problems
(1)
Prove that the equation has $x^2-x+3-ps=0$ with $x,s\in\mathbb{Z}$ has solutions
Source: Moldova TST 1995
8/8/2023
Let
p
p{}
p
be a prime number. Prove that the equation has
x
2
−
x
+
3
−
p
s
=
0
x^2-x+3-ps=0
x
2
−
x
+
3
−
p
s
=
0
with
x
,
s
∈
Z
x,s\in\mathbb{Z}
x
,
s
∈
Z
has solutions if and only if the equation
y
2
−
y
+
25
−
p
t
=
0
y^2-y+25-pt=0
y
2
−
y
+
25
−
pt
=
0
with
y
,
t
∈
Z
y,t\in\mathbb{Z}
y
,
t
∈
Z
has solutions.
number theory
prime numbers