Final answer:
The question involves finding a number that satisfies a system of congruences, which can be solved using the Chinese Remainder Theorem. The conditions are that the number leaves specific remainders when divided by 3, 5, and 7.
Step-by-step explanation:
The student is looking for a number that fulfills three different modular conditions: it leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 2 when divided by 7. This kind of problem is commonly solved using the Chinese Remainder Theorem, which is a method for solving systems of simultaneous congruences with different moduli.
To find such a number, we'd need to solve the system of congruences:
- x ≡ 2 (mod 3)
- x ≡ 3 (mod 5)
- x ≡ 2 (mod 7)
Without providing the detailed calculation here, which involves finding a common solution to these congruences, we can say that the smallest positive integer that satisfies all these conditions would be the answer to this problem.