AbstractThe following two facts are shown: 1.(i) There is a computable constant γ > 0 such that, given p0, there is a prime p > p0 satisfying p2|(km) for sufficiently large m, and 0≤k≤m with |m−2k| < m12 + γ (thus proving a conjecture of Erdős).2.(ii) For a positive integer a and a prime p, we have card{n<N: pa|(n2n)} ∼ N
AbstractWe prove that for almost all n, the numerator of the Bernoulli number B2n is divisible by a ...
AbstractErdős estimated the maximal number of integers selected from {1,2,…,N}, so that none of them...
AbstractLet x1,…,xr be a sequence of elements of Zn, the integers modulo n. How large must r be to g...
AbstractGiven a positive integer l, this paper establishes the existence of constants η > 1 and δ > ...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractIn this paper, we prove two results. The first theorem uses a paper of Kim (J. Number Theory...
AbstractIt is known that for sufficiently large n and m and any r the binomial coefficient (nm) whic...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractLet n be a positive integer and let A = {a1,…, as}, B = {b1,…, bt} be two sets of positive i...
If $a>b$ and $n>1$ are positive integers and $a$ and $b$ are relatively prime integers, then a large...
Let $n$ be a primitive non-deficient number where $n=p_1^{a_1}p_2^{a_2} \cdots p_k^{a_k}$ where $p_1...
AbstractThe Erdős–Moser conjecture states that the Diophantine equation Sk(m)=mk, where Sk(m)=1k+2k+...
AbstractA sequence A = {ai} of positive integers a1 < a2 < ⋯ is said to be primitive if no term of A...
AbstractIt is proved that every sufficiently large odd integer n can be written as n=x+p13+p23+p33+p...
AbstractWe prove that for almost all n, the numerator of the Bernoulli number B2n is divisible by a ...
AbstractErdős estimated the maximal number of integers selected from {1,2,…,N}, so that none of them...
AbstractLet x1,…,xr be a sequence of elements of Zn, the integers modulo n. How large must r be to g...
AbstractGiven a positive integer l, this paper establishes the existence of constants η > 1 and δ > ...
AbstractWe prove that for any integer d multinomial coefficients satisfying some conditions are exac...
AbstractIn this paper, we prove two results. The first theorem uses a paper of Kim (J. Number Theory...
AbstractIt is known that for sufficiently large n and m and any r the binomial coefficient (nm) whic...
AbstractA lower bound of Richert on the number of solutions of N − p = P3 is improved
AbstractWinkler has proved that, if n and m are positive integers with n ≤ m ≤ n25 and m ≡ n (mod 2)...
AbstractLet n be a positive integer and let A = {a1,…, as}, B = {b1,…, bt} be two sets of positive i...
If $a>b$ and $n>1$ are positive integers and $a$ and $b$ are relatively prime integers, then a large...
Let $n$ be a primitive non-deficient number where $n=p_1^{a_1}p_2^{a_2} \cdots p_k^{a_k}$ where $p_1...
AbstractThe Erdős–Moser conjecture states that the Diophantine equation Sk(m)=mk, where Sk(m)=1k+2k+...
AbstractA sequence A = {ai} of positive integers a1 < a2 < ⋯ is said to be primitive if no term of A...
AbstractIt is proved that every sufficiently large odd integer n can be written as n=x+p13+p23+p33+p...
AbstractWe prove that for almost all n, the numerator of the Bernoulli number B2n is divisible by a ...
AbstractErdős estimated the maximal number of integers selected from {1,2,…,N}, so that none of them...
AbstractLet x1,…,xr be a sequence of elements of Zn, the integers modulo n. How large must r be to g...
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