1. Zadatak

Prvi način:

$$12345^2+12353^2-2\cdot12349^2=$$ $$=12345^2-12349^2+12353^2-12349^2=$$ $$=(12345-12349)\cdot(12345+12349)+(12353-12349)\cdot(12353+12349)=$$ $$=-4\cdot24694+4\cdot24702=$$ $$=4\cdot(24702-24694)=$$ $$=4\cdot8=32$$

Drugi način:

$$12345^2+12353^2-2\cdot12349^2=$$ $$=(12349-4)^2+(12349+4)^2-2\cdot12349^2=$$ $$=12349^2-2\cdot12349\cdot4+4^2+12349^2+2\cdot12349\cdot4+4^2-2\cdot12349^2=$$ $$=16+16=32$$

Treći način:

$$12345^2=152399025$$ $$12353^2=152596609$$ $$12349^2=152497801$$ $$12345^2+12353^2-2\cdot12349^2=152399025+152596609-2\cdot152497801=$$ $$=32$$

Četvrti način:

$$12345^2+12353^2-2\cdot12349^2=$$ $$=12345^2+(12345+8)^2-2\cdot(12345+4)^2=$$ $$=12345^2+12345^2+2\cdot12345\cdot8+8^2-2\cdot(12345^2+2\cdot12345\cdot4+4^2)=$$ $$=2\cdot12345^2+16\cdot12345+64-2\cdot12345^2-16\cdot12345-32=$$ $$=64-32=32$$