Remainders
12 lessons · 10 questions · 5 PYQs
What the exams ask here
- remainder of a^n by 7, 9, 11, 13, 17
- 11^1011 + 1011^11 mod 9 (Indore 2025 Q3); (29^29)^29 mod 9 (Indore 2019 Q23); 7^103 + 7^101 mod 9 (Indore 2026)
- 1! + 2! + ... + 95! mod 15 (Indore 2023 Q8)
- quotient x remainder = 24, sum 10, divisor 5 -> dividend (Indore 2020 Q1); N = 36k + 14 -> N mod 24
- (p-1)! mod p (Wilson)
- 123456...4950 mod 16 / 9 / 11
- 1 + a + a^2 + ... + a^n mod m
Lessons
- Start hereThe idea and the methodFirst lesson of Remainders
- 1.Cyclicity: shrink the huge powerNew numbers every time (templates)5 min video
- 2.Negative Remainder: fix the minus signNotes only4 min video
- 3.Binomial trick1 question
- 4.Fermat small1 question
- 5.Successive division1 question
- 6.Sum of factorials2 questions + fresh variantsIndore 2023 SA
- 7.Large power mod 93 questions + fresh variantsIndore 2025
- 8.Division algorithm relations1 question + fresh variantsIndore 2020 SA
- 9.Wilson's Theorem: 150! mod 1511 question + fresh variants4 min video
- 10.Concatenated number remainderNew numbers every time (templates)
- 11.Geometric sum remainderNew numbers every time (templates)4 min video