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a_i \equiv i^2 mod 12 for all 1 <= i <= 11

Source: 2015 Saudi Arabia Pre-TST 2.4

September 12, 2020
number theory

Problem Statement

How many sequences of integers 1≤a1≤a2≤...≤a11≤20151 \le a_1 \le a_2\le ... \le a_{11 }\le 2015 that satisfy ai≡i2a_i \equiv i^2 (mod 1212) for all 1≤i≤111 \le i \le 11 are there?
(Le Anh Vinh)
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