设a为质数,b为正整数,且9(2a+b)(2)=509(4a+511b),求a,b值.解题方法:、509是质数,2a+b为509的整数倍,设2a+b=509K(K为整数) 代入,得:9KK*509*509=509(509b+2*509k) 9KK=b+2K=509K-2a+2K 2a=(511-9K)k 因为a是质数,所以K=1或51
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![设a为质数,b为正整数,且9(2a+b)(2)=509(4a+511b),求a,b值.解题方法:、509是质数,2a+b为509的整数倍,设2a+b=509K(K为整数) 代入,得:9KK*509*509=509(509b+2*509k) 9KK=b+2K=509K-2a+2K 2a=(511-9K)k 因为a是质数,所以K=1或51](/uploads/image/z/6859626-42-6.jpg?t=%E8%AE%BEa%E4%B8%BA%E8%B4%A8%E6%95%B0%2Cb%E4%B8%BA%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E4%B8%949%282a%2Bb%29%282%29%3D509%284a%2B511b%29%2C%E6%B1%82a%2Cb%E5%80%BC.%E8%A7%A3%E9%A2%98%E6%96%B9%E6%B3%95%3A%E3%80%81509%E6%98%AF%E8%B4%A8%E6%95%B0%2C2a%2Bb%E4%B8%BA509%E7%9A%84%E6%95%B4%E6%95%B0%E5%80%8D%2C%E8%AE%BE2a%2Bb%3D509K%EF%BC%88K%E4%B8%BA%E6%95%B4%E6%95%B0%EF%BC%89+%E4%BB%A3%E5%85%A5%2C%E5%BE%97%3A9KK%2A509%2A509%3D509%28509b%2B2%2A509k%29+9KK%3Db%2B2K%3D509K-2a%2B2K+2a%3D%28511-9K%29k+%E5%9B%A0%E4%B8%BAa%E6%98%AF%E8%B4%A8%E6%95%B0%2C%E6%89%80%E4%BB%A5K%3D1%E6%88%9651)
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