# Under modular conditions

Number Theory Level 3

a is a positive integer less than 100.

a $$\equiv$$ 2 (mod 5)

a $$\equiv$$ 1 (mod 13)

a $$\equiv$$ -4 (mod 12)

a $$\equiv$$ n (mod 94) where n is an integer and -45<n<51. What is the largest possible value of n?

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