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JEE Advanced Mathematics question

MathematicsBasic Mathematics and LogarithmJEE Advanced

Let be divisible by 4, where are digits. The largest possible number of values of is .

Answer: 45000

Solution

Work modulo 4 (each ):

3 ≡ -1, 5 ≡ 1, 7 ≡ -1, 9 ≡ 1 ±od 4,

so

E ≡ + (- + 1 + (- + 1 ±od 4.

Let ; iff have opposite parity.

- : , which is odd

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Question ID VK-110310