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  • Fill in each blank with an answer as easy as possible.

    Fill in each blank with an answer as easy as possible.
    (a)M is a triangular number if and only if___________ is an odd square number.
    (b)N is an odd square number if and only if____________is a triangular number.
    triangular number:n(n+1)/2,square number:n^2.
    英語人氣:639 ℃時(shí)間:2020-06-03 13:10:38
    優(yōu)質(zhì)解答
    (a)
    M = n(n+1)/2
    等價(jià)于:8M+1 = 4 n^2 + 4 n + 1 = (2n+1)^2
    所以,第1個(gè)空應(yīng)該填:8M+1
    (b)
    N = (2n+1)^2
    等價(jià)于:(N-1) / 8 = n(n+1)/2
    所以,第2個(gè)空應(yīng)該填:(N-1)/8
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