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Gupta, Hansraj
- A Note on the Parity of P(n)
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The Journal of the Indian Mathematical Society, Vol 10 (1946), Pagination: 32-33Abstract
In 1920, Mac Mahon* gave a method for determining the parity of p(n)-the number of unrestricted partitions of n. He made use of Jacobi's Elliptic products. His results are here obtained in a simpler and more direct way.- An Asymptotic Formula in Partitions
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1 Hoshiarpur, IN
1 Hoshiarpur, IN
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The Journal of the Indian Mathematical Society, Vol 10 (1946), Pagination: 73-76Abstract
In what follows, p(n, m) denotes the number oi partitions of n into exactly m non-zero summands and p0(n) the number of unrestricted partitions of n.- A Congruence Relation between τ(n) and σ(n)
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1 Government College, Hoshiarpur, IN
1 Government College, Hoshiarpur, IN
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The Journal of the Indian Mathematical Society, Vol 9 (1945), Pagination: 59-60Abstract
Proceeding on the lines of my paper (1) on the "Congruence Properties of τ(n)", it can be shown that for any odd prime p,
σ (P) = P+I (mod 8)
= σ(P) (mod 8),
where τ(n) is Ramanujan's function.
- On Numbers in Medial Progression
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1 Government College, Hoshiarpur, IN
1 Government College, Hoshiarpur, IN
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The Journal of the Indian Mathematical Society, Vol 19 (1932), Pagination: 203-214Abstract
A sequence of numbers al= a2, a3, • an,••• is said to be in Medial Progression (M.P.)if ar = ar_1 +ar-2 [r≥3]. … (1)
Throughout this paper which develops properties of such a progression, the numbers an will be supposed to be positive or negative integers.
- A Formula for L(n)
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1 Hoshiarpur, IN
1 Hoshiarpur, IN
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The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 68-71Abstract
In what follows, all small letters denote integers ≥ o; the letter m is used to denote only quadratfrei numbers; p denotes any prime; pv the vth prime with p1 = 2. Q(pv) denotes the set of quadratfrei integers none of whose prime factors exceeds pv.- On the Maximum Values of Pk(n) and πk(n)
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1 Govt. College, Hoshiarpur, IN
1 Govt. College, Hoshiarpur, IN
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The Journal of the Indian Mathematical Society, Vol 7 (1943), Pagination: 72-75Abstract
If pk(n) denotes the number of partitions of n into k non-zero summands, then I have shown that for all positive integral values of n ≥ k.- A Formula in Partitions
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1 Hoshiarpur, IN
1 Hoshiarpur, IN
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The Journal of the Indian Mathematical Society, Vol 6 (1942), Pagination: 115-117Abstract
In what follows, Pm(n) denotes the number of those partitions of n in which the smallest element is m; pm(n) the number of those in which m is the largest element, i.e. the number of partitions of n into exactly m non-zero parts; and p(n) denotes the number of unrestricted partitions of n.- Some Properties of Generalised Combinatory Functions
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1 Government College, Hoshiarpur, IN
1 Government College, Hoshiarpur, IN
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The Journal of the Indian Mathematical Society, Vol 5 (1941), Pagination: 27-31Abstract
Throughout this paper, p denotes an odd prime; all other small letters except x, denote integers ≥0, unless stated otherwise. Φ is Euler's function. The symbol " < " is read "less than and prime to."- On Numbers of the Form 4a(8b+7)
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1 Hoshiarpur, IN
1 Hoshiarpur, IN