Question

Prove that 1 * 3 * 5 * ... * 2345 + 2 *4 * 6* ... * 3456 is divisible by 6789.

Answer 1

6789 = 3*31*73

since 3,31,73 all divide the first term,
and 6,62,146 all divide the second term,

6789 divides both terms, and thus the sum as well.

Answer 2

6789 = 3*31*73

since 3,31,73 all divide the first term,
and 6,62,146 all divide the second term,

6789 divides both terms, and thus the sum as well.

Answer 3

For the above responses:
idk how do you conclude that 'if a|b and a|c ⇒ a|(b+c)'. The general true statement is 'if a|b and a|c ⇒ a|(bx+cy)'.

Answer 4

Idk