A number theory problem by Wildan Bagus Wicaksono
Determine the value of
2 0 1 7 ⋅ 4 0 3 5 + 2 0 1 8 2 2 0 1 7 3 − 2 0 1 8 3
The answer is -1.
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2 solutions
= 2 0 1 7 ⋅ 4 0 3 5 + 2 0 1 8 2 2 0 1 7 3 − 2 0 1 8 3 = 2 0 1 7 ( 2 0 1 7 + 2 0 1 8 ) + 2 0 1 8 2 2 0 1 7 3 − 2 0 1 8 3 = 2 0 1 7 2 + 2 0 1 7 ⋅ 2 0 1 8 + 2 0 1 8 2 2 0 1 7 3 − 2 0 1 8 3 = 2 0 1 7 2 + 2 0 1 7 ⋅ 2 0 1 8 + 2 0 1 8 2 ( 2 0 1 7 2 + 2 0 1 7 ⋅ 2 0 1 8 + 2 0 1 8 2 ) ( 2 0 1 7 − 2 0 1 8 ) = − 1
Oh, sorry. thanks for the correction
Question posted is wrong. There should be minus sign in numerator but there is plus sign. Pls change the question
Let n = 2 0 1 7 .
N = n ( 2 n + 1 ) + ( n + 1 ) 2 n 3 − ( n + 1 ) 3 = n ( 2 n + 1 ) + ( n + 1 ) 2 [ n − ( n + 1 ) ] [ n 2 + n ( n + 1 ) + ( n + 1 ) 2 ] = ( − 1 ) n ( 2 n + 1 ) + ( n + 1 ) 2 n ( 2 n + 1 ) + ( n + 1 ) 2 = − 1 a 3 − b 3 = ( a − b ) ( a 2 + a b + b 2 )