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Chowla, S. D.
- On the Largest Prime Divisors of Numbers
Authors
Source
The Journal of the Indian Mathematical Society, Vol 11 (1947), Pagination: 31-37Abstract
The object of this note is to give an answer to the
QUERY: Let g(m) denote the largest prime divior of m. In what range does g(m) lie for all almost all values of m ≤ x?
More precisely, suppose that h(x) and H(x) aie two functions of x; let N(x) = N(h, H x) denote the number of numbers m ≤ x for which h(x) ≤ g(m) ≤ H(x). For what choices of h(x) and H(x) can we say that N(x)/x→I, as x→∞?.
- On a Certain Limit Connected with Pairs of Integers
Authors
1 Punjab University, IN
Source
The Journal of the Indian Mathematical Society, Vol 18 (1930), Pagination: 13-15Abstract
Let us denote by { m, n } the number of distinct pairs of integers, r and s, such that* (r, s) = 1,
1 ≤ r ^ m,
1 ≤ s ^ n.
- On the Greatest Prime Factor of a Certain Product
Authors
Source
The Journal of the Indian Mathematical Society, Vol 18 (1930), Pagination: 135-137Abstract
Let Px denote the greatest prime factor of the product
f(x) = (1 + 12) (1 + 22) (1 + x2).
- An Order Result Involving Euler's .φ-Function
Authors
Source
The Journal of the Indian Mathematical Society, Vol 18 (1930), Pagination: 138-141Abstract
It is well known that
X ∑1 φ(n)= 3/π2X2+O(X log X).
1 where φ is the number of positive integers less than and prime to.
- On the Order of N (R), the Number of Terms in the Period of the Continued Fraction for √R.
Authors
Source
The Journal of the Indian Mathematical Society, Vol 18 (1930), Pagination: 142-144Abstract
Let us denote by N (R) the number of terms in the perie^ of the simple continued fraction for √R, where R is a positive integer. Dr. T. Vijayaraghavan has recently.- Expressions for the Class Number of Binary Quadratic Forms
Authors
Source
The Journal of the Indian Mathematical Society, Vol 18 (1930), Pagination: 145-146Abstract
Hacks has found that the number of properly primitive classes of negative determinant - q, where q is a prime of the form 4n + 3 is where [*] denotes the greatest integer contained in x.- Cauchy's Criterion for the Solvability of Xp + YpZp in Integers Prime to P
Authors
Source
The Journal of the Indian Mathematical Society, Vol 18 (1930), Pagination: 205-206Abstract
Cauchy stated, and it is not yet prqred, that if the equation Xp + Yp = Zp has any solutions in integers all prime to p, then
θ∑n=1 np-4=O(mod p) … (1.1)
where θ= [1/2p]; [x] denotes the greatest integer contained in.