MathDB
Problems
Contests
International Contests
IMO Longlists
1976 IMO Longlists
18
18
Part of
1976 IMO Longlists
Problems
(1)
Proving that a number is divisible by 4th Fermat prime F_4
Source:
1/3/2011
Prove that the number
1
9
1976
+
7
6
1976
19^{1976} + 76^{1976}
1
9
1976
+
7
6
1976
:
(
a
)
(a)
(
a
)
is divisible by the (Fermat) prime number
F
4
=
2
2
4
+
1
F_4 = 2^{2^4} + 1
F
4
=
2
2
4
+
1
;
(
b
)
(b)
(
b
)
is divisible by at least four distinct primes other than
F
4
F_4
F
4
.
number theory unsolved
number theory