Prove that there are infinitely many natural numbers a with the following property: thenumber z = n'+a is not prime for any natural number n.(GDR)1.证明:存在无穷多个正整数a,使得数列 (z_n)_(n≥1),z_n=n^4+a 不包含任何素数(东德) 答案 【解析】1.解法一考虑所有形如 n^4+a , n...
b are simultaneously rational ask question asked 7 months ago modified 7 months ago viewed 66 times 3 the question prove that there are infinitely many distinct natural numbers a , b a , b for which a + b − − − − √ , a − b − − − − √ a...
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结果1 题目 3.Prove that there exist infinitely many positive integers n such that n'+1 has a prime divi- sor which is greater than 2n 十√2n. (LTU) 3.证明:存在无穷多个正整数n,使得n'+1 有一个大于 2n 2n+ √(2n) 因子. (立陶宛) 相关知识点: 试题来源: 解析 ...
Prove that there are infinitely many primes with remainder of 3 when divided by 4. Prove the following statement. When n=2p, where P is an odd prime,. Then a^{n-1}= a(mod \ n) for any integer a. Find the prime factorization for ...
QUESTION : Let a,ba,b be positive integers such that a∣b2,b2∣a3,a3∣b4…a∣b2,b2∣a3,a3∣b4…...so on, then prove that a=ba=b This is what I tried: Say a≠ba≠b rather than a>b≥1a>b≥1 ∃k:ak−1>bk∃k:ak−1>bk Then: ak−1>bkak−1>bk...