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VMEO = Vietnam Mathematical E-Olympiad
VMEO IV 2015
12.3
VMEO IV P3/12 - Junior Division
VMEO IV P3/12 - Junior Division
Source:
May 14, 2016
number theory
arithmetic sequence
prime numbers
Problem Statement
Find all integes
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
that form an arithmetic progression satisfying
d
ā
c
+
1
d-c+1
d
ā
c
+
1
is prime number and
a
+
b
2
+
c
3
=
d
2
b
a+b^2+c^3=d^2b
a
+
b
2
+
c
3
=
d
2
b
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