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  • 1) the sum of the three smallest primes and one other prime is 77.what is the product of these four primes?

    1) the sum of the three smallest primes and one other prime is 77.what is the product of these four primes?
    2)what are both integers n for which (2^n^4)(2^n^3)(2^n^2)(2^N)=1?(里面的2^n^4代表2的n次方又n的4次方)..
    英語(yǔ)人氣:356 ℃時(shí)間:2020-01-28 22:23:17
    優(yōu)質(zhì)解答
    1) 最小的3個(gè)質(zhì)數(shù)和一天其他質(zhì)數(shù)的和是77,求這4個(gè)質(zhì)數(shù)的積.
    The three smallest primes are 2,3,and 5.So the 4th prime is 77-2-3-5=67.Their product is 2*3*5*67=2010.
    2) 滿足等式(2^n^4)(2^n^3)(2^n^2)(2^N)=1的兩個(gè)整數(shù)是什么?
    (2^n^4)(2^n^3)(2^n^2)(2^N)=2^(n^4+n^3+n^2+n),
    Because 2^0=1,n^4+n^3+n^2+n must be 0.
    n^4+n^3+n^2+n=n(n^3+n^2+n+1)=n*(n+1)*(n^2+1) must be 0.
    It's easy to see either n=0 or n+1=0.
    So the answer is n=0 or n=-1.
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