The sum of 123 + 2 times 123 + 3 times 123 +. + 123 times 123 divided by 7 is the remainder

The sum of 123 + 2 times 123 + 3 times 123 +. + 123 times 123 divided by 7 is the remainder

123 + 2 times 123 + 3 times 123 +. + 123 times 123 = 123 + 2 × 123 + (3 + 123) × 123 + (4 + 122) × 123 + (5 + 121) × 123 +... + (62 + 64) × 123 + 63 × 123 = 3 × 123 + (3 + 123) × 123 + (4 + 122) × 123 +... + (62 + 64) × 123 + 63 × 123 (*) (*) where (3 + 123) ×

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