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一个有趣数论题:设m=a²+1>5,

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a∈Z,m的个位数不是7,则m是合数。


IP属地:贵州来自Android客户端1楼2024-06-01 20:23回复
    a²+1是素数,素数大于5的都是奇数,
    a²+1是奇数,a是偶数,a的个位是2或8时m的个位是5是合数,a的个位是4或6时m的个位是7,a个位数只能是0,m的个位是1,然后就找(10a)²+1是素数的数。


    IP属地:安徽来自Android客户端2楼2024-06-01 20:43
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      还可能是1呀,a=10时a²+1=101是素数


      IP属地:北京来自Android客户端3楼2024-06-02 09:52
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        2024-06-05 09:30:12
        a = 1, (10a)^2 + 1 is prime
        a = 2, (10a)^2 + 1 is prime
        a = 4, (10a)^2 + 1 is prime
        a = 9, (10a)^2 + 1 is prime
        a = 11, (10a)^2 + 1 is prime
        a = 12, (10a)^2 + 1 is prime
        a = 13, (10a)^2 + 1 is prime
        a = 15, (10a)^2 + 1 is prime
        a = 16, (10a)^2 + 1 is prime
        a = 17, (10a)^2 + 1 is prime
        a = 18, (10a)^2 + 1 is prime
        a = 21, (10a)^2 + 1 is prime
        a = 23, (10a)^2 + 1 is prime
        a = 24, (10a)^2 + 1 is prime
        a = 25, (10a)^2 + 1 is prime
        a = 26, (10a)^2 + 1 is prime
        a = 27, (10a)^2 + 1 is prime
        a = 28, (10a)^2 + 1 is prime
        a = 30, (10a)^2 + 1 is prime
        a = 34, (10a)^2 + 1 is prime
        a = 35, (10a)^2 + 1 is prime
        a = 40, (10a)^2 + 1 is prime
        a = 42, (10a)^2 + 1 is prime
        a = 43, (10a)^2 + 1 is prime
        a = 44, (10a)^2 + 1 is prime
        a = 47, (10a)^2 + 1 is prime
        a = 49, (10a)^2 + 1 is prime
        a = 57, (10a)^2 + 1 is prime
        a = 68, (10a)^2 + 1 is prime
        a = 69, (10a)^2 + 1 is prime
        a = 70, (10a)^2 + 1 is prime
        a = 74, (10a)^2 + 1 is prime
        a = 75, (10a)^2 + 1 is prime
        a = 76, (10a)^2 + 1 is prime
        a = 78, (10a)^2 + 1 is prime
        a = 86, (10a)^2 + 1 is prime
        a = 89, (10a)^2 + 1 is prime
        a = 91, (10a)^2 + 1 is prime
        a = 92, (10a)^2 + 1 is prime
        a = 93, (10a)^2 + 1 is prime
        a = 95, (10a)^2 + 1 is prime
        a = 96, (10a)^2 + 1 is prime
        用时 0.000000 秒


        IP属地:浙江4楼2024-06-05 09:32
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          疏忽了,只算个位是1,2,3→9的情况,忘记了还有0。所以排除a被10整除的就好了。


          IP属地:贵州来自Android客户端5楼2024-06-05 10:01
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            a^2+1个位数为,0,1,2,5,6,7,1和7都有可能是素数


            IP属地:重庆来自Android客户端6楼2024-06-05 19:31
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