Diophantine Equations in IOQM: previous year question analysis
Diophantine Equations has appeared 39 times in IOQM between 2012 and 2025, making it the 5th most-asked of 14 chapters and about 11% of the bank. Over the last 5 years it has averaged 3.6 questions per year.
Total PYQs
39
Years covered
2012–2025
Weightage rank
#5 of 14
Share of bank
11%
How many Diophantine Equations questions appeared each year
| Year | Questions | Relative volume |
|---|---|---|
| 2013 | 1 | |
| 2014 | 2 | |
| 2015 | 3 | |
| 2016 | 3 | |
| 2017 | 2 | |
| 2018 | 3 | |
| 2019 | 3 | |
| 2021 | 2 | |
| 2022 | 4 | |
| 2023 | 3 | |
| 2024 | 2 | |
| 2025 | 7 |
Which Diophantine Equations sub-topics are asked most
Every question in this chapter is tagged to a sub-topic, so you can see exactly where the marks sit before you revise.
- linear Diophantine equation, counting solutions1 questions
- system of equations in whole numbers1 questions
- perfect square condition, difference of squares factorisation1 questions
- quadratic Diophantine equation, factorisation / discriminant1 questions
- integer word problem with divisibility constraints1 questions
- gcd equation in natural numbers1 questions
- integer solution from fractional-share constraints1 questions
- integer solutions of a symmetric rational equation1 questions
- Pythagorean triples containing a given leg1 questions
- system in powers of 3 and 21 questions
Question formats used in Diophantine Equations
- Numerical / integer answer39
How Diophantine Equations compares with nearby chapters
- #3Polynomials & Equations43
- #4Divisibility & Primes41
- #5Diophantine Equations39
- #6Quadrilaterals & Polygons28
- #7Digits & Base Systems27
Counts are computed from AcadXL’s own IOQM question bank, tagged chapter- and sub-topic-wise and checked against official answer keys. Sign in to attempt the 39 Diophantine Equations questions with solutions.