1³ 2³ 3³ ......99³ last digit number
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Use the identity
a³+b³=(a+b)(a²−ab+b²) Hence,,
a³+(99−a)³=99[a²−a(99−a)+(99−a)²] That is, each of the pairs 13+983,23+973,…493+503 is divisible by 99 . Since 993 is also divisible by 99 , so is the sum.
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