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Eotvos Mathematical Competition (Hungary)
1899 Eotvos Mathematical Competition
3
Prove that, for any natural number $n$, the expression $$A = 2903^n-803^n-464^n+
Prove that, for any natural number $n$, the expression $$A = 2903^n-803^n-464^n+
Source: Eotvos 1899 p3
March 15, 2020
algebra
Problem Statement
Prove that, for any natural number
n
n
n
, the expression
A
=
290
3
n
−
80
3
n
−
46
4
n
+
26
1
n
A = 2903^n-803^n-464^n+261^n
A
=
290
3
n
−
80
3
n
−
46
4
n
+
26
1
n
is divisible by
1897
1897
1897
.
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