西南大学[0346]《初等数论》数论作业4
西南大学《初等数论》数论作业4证明题
1. 证明：若a，b都是m的倍数，则data:image/png;base64,R0lGODlhJAATAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIABAAgAAsAhAAAAAAAAAAAHR0AAB0AHQAAMx0AMgAcSAAzWh1GbDMAADIAMjNdXTNbgEgcAEceM1ozHVozAEZGM1lZf1l/WUhuf11/f2xGHX9/XX9uSGaIiIBbM4iIZgECAwECAwECAwVPICCOZGmawamuJ8S+7AKrz1xegQAcdskoqZEDIVKsaipFQTQQRUqNUmBKDY42JEV0OTIcVc8RQUQUOXokmXNdtJ6QJazowgVMl0q0c0oKAQA7也是m的倍数。
2. 设n是整数，证明3 | n(n + 1)(n + 2)。
3. 设n是整数，证明：data:image/png;base64,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。设x，y均为整数。
4. 证明：若data:image/png;base64,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，则data:image/png;base64,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。
5. 设x，y均为整数。证明：若data:image/png;base64,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，则data:image/png;base64,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。
6. 证明：若k是整数，则data:image/png;base64,R0lGODlhQQAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAwA9AA4AhAAAAAAAAB0AAB0AHQAAHR0AMgAAMwAcSB0dSAAzWh1GbDMAADIAHTIAMjMzWzNbgEgcAEceM1ozHVozAFtISEhIW11/f0huf2xGHW5GRn9/XX9uSGaIiIBbM4iIZgECAwWGICCOJLAEZaqubOuWzSvPdG3f5clSuIn2kBRj1emJhrjToYRQFY2AZivCwpSsKUxg28Mal6QHQMCFhsflEnXlFRXMq7drvQIDrBvbdp8W4VUTfHsJVySBAQZwhluJPXZDGwMXikcAkZMrdFkjTwBBlJ2fmS12CiMBBJhmpiKoqiSaJCeoACEAOw==是奇数。
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