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True or False?
There exist distinct positive integers aaa and bbb such that a100+b100a^{100}+b^{100}a100+b100 is divisible by all of the following numbers: a+b,a2+b2,a3+b3,a4+b4,…,a99+b99,a100+b100.a+b, a^2+b^2, a^3+b^3, a^4+b^4, \ldots, a^{99}+b^{99}, a^{100}+b^{100}.a+b,a2+b2,a3+b3,a4+b4,…,a99+b99,a100+b100.
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