It is known that the nth power of (1 + x) + (1 + x) +. + (1 + x) = A0 + A1 + A2 +... + an. If A0 + A1 + A2 +... + an. = 30, what is the natural number n?

It is known that the nth power of (1 + x) + (1 + x) +. + (1 + x) = A0 + A1 + A2 +... + an. If A0 + A1 + A2 +... + an. = 30, what is the natural number n?


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If A1, A2 An is 1, 2 Then (A1-1) (A2-2) (an-n) is even


Proof: A1, A2 An is 1, 2 , any permutation of n (n is odd), a1 + A2 + +an=1+2+… +n，∴（a1-1）+（a2-2）+… +(an-n) = 0 is an even number,... (A1-1), (A2-2) At least one of (an-n) must be even It is proved that (an-n) is even

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