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Sambasiva Rao, K.
- On the Probability that Two kth Power-Free Integers Belonging to an Assigned Arithmetic Progression should be Prime to One Another
Authors
1 Andhra University, IN
Source
The Journal of the Indian Mathematical Society, Vol 9 (1945), Pagination: 88-92Abstract
Hardy and Wright derived the probability that two integers should be relatively prime from the asymptotic formula for
Σ Φ(n).
- On Waring's Problem for Smaller Powers
Authors
1 Andhra University, IN
Source
The Journal of the Indian Mathematical Society, Vol 5 (1941), Pagination: 117-121Abstract
In a manuscript, L. K. Hua has proved, among other things, that
G(5) ≤ 24, G(6) ≤ 37 and G(7) ≤ 53,
these being improvements on my results. Before the receipt of Hua's manuscript, I had pointed out that G(5) ≤ 24. The main lemma of Hua's argument is aimed at improving the lower limits for Hs,k(N), the number of integers less than N and expressible as the sum of s positive kth powers.
- A Correction
Authors
Source
The Journal of the Indian Mathematical Society, Vol 4 (1940), Pagination: 125-125Abstract
In my paper 'On a particular representation of integers as sums of kth powers', the validity of the proof of Theorem 1 has been questioned in the review appearing in Mathematical Reviews.- On a Particular Representation of Integers as Sums of kth Powers
Authors
1 Andhra University, IN
Source
The Journal of the Indian Mathematical Society, Vol 3 (1939), Pagination: 262-265Abstract
Consider the following way of representation of any positive integer x in the form
x = xlk+xk2+...+xks, (1)
where x1, x2, ..., xs are integers given by
(x1+1)k > x ≥ x1k
(x2+1)k > x-x1k ≥ x2k (2)
................
.................
the process terminating with
(xs+1)k > x-x1k-xk2-........-xks-1 = xks.
It can easily be seen that there is one and only one way of representation of an integer x in this manner. The number of kth powers required in the representation of x in the above manner is clearly a function of x and k, and hence can be denoted by Sk(x).