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The problem specification indicates that all index pairs (i, j) where i < j and ar[i] + ar[j] is divisible by k must be found. Therefore, all possible pairs of elements in the array should be considered, as long as they meet the condition that i is less than j.

If we review the array [1, 3, 2, 6, 1, 2], the pairs are formed by checking each possible combination of indices (i, j) where i < j. In this case, the pair (4, 5) is also valid because:

ar[4] = 1 and ar[5] = 2
1 + 2 = 3, and 3 is divisible by 3.
So the pair (4, 5) also meets the condition.

Here is the complete list of pairs that meet the divisibility condition by 3:

In summary, the pair (4, 5) should also be considered, as it meets the conditions, so the result should be 6 and not 5.
Is there an error in the problem explanation and the result should be 6, or is the result indeed 5 and the condition that the pair (4, 5) was excluded not explained?
What is the exact criterion for evaluating the pairs to be considered?

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## Divisible Sum Pairs

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The problem specification indicates that all index pairs (i, j) where i < j and ar[i] + ar[j] is divisible by k must be found. Therefore, all possible pairs of elements in the array should be considered, as long as they meet the condition that i is less than j.

If we review the array [1, 3, 2, 6, 1, 2], the pairs are formed by checking each possible combination of indices (i, j) where i < j. In this case, the pair (4, 5) is also valid because:

ar[4] = 1 and ar[5] = 2 1 + 2 = 3, and 3 is divisible by 3. So the pair (4, 5) also meets the condition.

Here is the complete list of pairs that meet the divisibility condition by 3:

(0, 2) â†’ 1 + 2 = 3 (0, 5) â†’ 1 + 2 = 3 (2, 3) â†’ 2 + 6 = 8 (2, 4) â†’ 2 + 1 = 3 (3, 4) â†’ 6 + 1 = 7 (4, 5) â†’ 1 + 2 = 3

In summary, the pair (4, 5) should also be considered, as it meets the conditions, so the result should be 6 and not 5. Is there an error in the problem explanation and the result should be 6, or is the result indeed 5 and the condition that the pair (4, 5) was excluded not explained? What is the exact criterion for evaluating the pairs to be considered?