Rezolvare:
Scriem ipoteza problemei:
[tex]fie \: x \: numarul \: cautat \\ a \: b \: c \: - cele \: 3 \: caturi[/tex]
[tex]x \div 3 = a \: rest \: 2 \\ x \div 4 = b \: rest \: 3 \\ x \div 5 = c \: rest \: 4[/tex]
x = 3a+2 |+1
x = 4b+3 |+1
x = 5c+4 |+1
x+1 = 3a+3 = 3(a+1) = M3 (multiplu de 3)
x+1=4b+4=4(b+1)= M4
x+1=5b+5=5(b+1)=M5
Aflăm cel mai mic multiplu comun (C.M.M.M.C) al numerelor 3, 4, 5.
3 = 3¹
4 = 2²
5 = 5¹
C.M.M.M.C = 3¹×2²×5¹=60
Așadar x+1=30 => x = 59.
