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4
\sqrt{(20^n- 18^n)/ 19} is rational
\sqrt{(20^n- 18^n)/ 19} is rational
Source: 2018 Romanian NMO grade VII P4
September 4, 2024
rational
number theory
Problem Statement
Find the natural number
n
n
n
for which
2
0
n
−
1
8
n
19
\sqrt{\frac{20^n- 18^n}{19}}
19
2
0
n
−
1
8
n
is a rational number.
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