Question 260 · JIMS III, 43
Solution published in JIMS III (Collected Papers, 1927).
Ramanujan’s questions
Between 1911 and 1919 Srinivasa Ramanujan posed 58 questions in the Journal of the Indian Mathematical Society. Most have been solved; a few remain incompletely solved, and one, the Brocard–Ramanujan problem, is famously open.
28Solved2Partially solved1Open27Being verified
Solved
Question 261 · JIMS III, 43
Solution published in JIMS III (Collected Papers, 1927).
Question 283 · JIMS III, 89; IV, 106
Two solutions published in JIMS III (Collected Papers, 1927).
Question 284 · JIMS III, 89
Solved by Ramanujan himself, JIMS IV, 183.
Question 289 · JIMS III, 90
Solved by Ramanujan himself, JIMS IV, 226.
Question 294 · JIMS III, 128
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Question 295 · JIMS III, 128
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Question 308 · JIMS III, 166
Solution published in JIMS (Collected Papers, 1927).
Question 327 · JIMS III, 209
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Question 352 · JIMS IV, 40
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Question 353 · JIMS IV, 40
Solution published in JIMS VIII (Collected Papers, 1927).
Question 358 · JIMS IV, 78
Solution published in JIMS VII (Collected Papers, 1927).
Question 359 · JIMS IV, 78
Solution published in JIMS XV (Collected Papers, 1927).
Question 386 · JIMS IV, 120
Solution published in JIMS VII (Collected Papers, 1927).
Question 387 · JIMS IV, 120
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Question 427 · JIMS IV, 238
Two solutions published in JIMS X (Collected Papers, 1927).
Question 441 · JIMS V, 39
Solution published in JIMS VI (Collected Papers, 1927).
Question 463 · JIMS V, 120
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Question 464 · JIMS V, 120
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Question 469 · JIMS V, 159
The Brocard–Ramanujan problem: does n! + 1 = m² have solutions other than n = 4, 5, 7? Still open (also Erdős problem #398).
Question 489 · JIMS V, 200
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Question 507 · JIMS V, 240
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Question 524 · JIMS VI, 39
Solution published in JIMS VI (Collected Papers, 1927).
Question 525 · JIMS VI, 39
Solution published in JIMS VI (Collected Papers, 1927).
Question 526 · JIMS VI, 39
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Question 541 · JIMS VI, 79
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Question 546 · JIMS VI, 80
Solutions published in JIMS VII–VIII (Collected Papers, 1927).
Question 571 · JIMS VI, 160
Solution published in JIMS VII (Collected Papers, 1927).
Question 584 · JIMS VI, 199
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Question 605 · JIMS VI, 239
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Question 606 · JIMS VI, 239
Solution published in JIMS VII (Collected Papers, 1927).
Question 629 · JIMS VII, 40
Three solutions published in JIMS VIII (Collected Papers, 1927).
Question 642 · JIMS VII, 80
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Question 661 · JIMS VII, 119
Solutions published in JIMS XIII–XIV (Collected Papers, 1927).
Question 662 · JIMS VII, 119–120
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Question 666 · JIMS VII, 120
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Question 681 · JIMS VII, 160
Only a partial solution on record (N. B. Mitra, JIMS XIII; Collected Papers, 1927).
Question 682 · JIMS VII, 160
Solution published in JIMS X (Collected Papers, 1927).
Question 699 · JIMS VII, 199
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Question 700 · JIMS VII, 199
Two solutions published in JIMS VIII (Collected Papers, 1927).
Question 722 · JIMS VII, 240
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Question 723 · JIMS VII, 240
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Question 724 · JIMS VII, 240
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Question 738 · JIMS VIII, 40
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Question 739 · JIMS VIII, 40
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Question 740 · JIMS VIII, 40
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Question 753 · JIMS VIII, 80
Two solutions published in JIMS X (Collected Papers, 1927).
Question 754 · JIMS VIII, 80
Only a partial solution on record (K. B. Madhava, JIMS XII; Collected Papers, 1927).
Question 755 · JIMS VIII, 80
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Question 768 · JIMS VIII, 119
Solution, with correction, published in JIMS VIII (Collected Papers, 1927).
Question 769 · JIMS VIII, 120
Solution, with correction, published in JIMS IX (Collected Papers, 1927).
Question 770 · JIMS VIII, 120
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Question 783 · JIMS VIII, 159
Proved and generalized by Berndt and Evans (1990).
Question 784 · JIMS VIII, 159
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Question 785 · JIMS VIII, 159–160
Solution published in JIMS (Collected Papers, 1927).
Question 1049 · JIMS XI, 120
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Question 1070 · JIMS XI, 160
Solution published in JIMS XII (Collected Papers, 1927).
Question 1076 · JIMS XI, 199
Proved by Berndt, Chan and Zhang, 'Radicals and units in Ramanujan's work', who also correct a misprint in the original statement.
Sources
Questions: Collected Papers of Srinivasa Ramanujan, Questions in JIMS (Institute of Mathematical Sciences, Chennai).
Survey: B. C. Berndt, Y.-S. Choi and S.-Y. Kang, “The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society”, in Ramanujan: Essays and Surveys (AMS, 2001).
“Solved” and “Partially solved” follow the solution notes in Ramanujan’s Collected Papers (1927) and the later literature cited on each question. “Being verified” means we have not yet confirmed the status against the survey.