MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2019 Korea National Olympiad
3
3
Part of
2019 Korea National Olympiad
Problems
(1)
Residues
Source: Korean National Olympiad 2nd Round 2019 #3
11/16/2019
Suppose that positive integers
m
,
n
,
k
m,n,k
m
,
n
,
k
satisfy the equations
m
2
+
1
=
2
n
2
,
2
m
2
+
1
=
11
k
2
.
m^2+1=2n^2, 2m^2+1=11k^2.
m
2
+
1
=
2
n
2
,
2
m
2
+
1
=
11
k
2
.
Find the residue when
n
n
n
is divided by
17
17
17
.
number theory