find a number that divide 37,67,97 reminders will be 1,2,3 respectively.

• N should divide
  (37-1)
  (67-2)
  (97-3)
• 7 years agoHelpfull: Yes(0) No(1)
• 37,67,97
  x =1074+2479v=1074+2479(61+97w)=1074+151219+240463w=152293+240463w
  
  So 152293 , or 152293 plus a multiple of 240463 are the only numbers which leave all the wanted remainders.
  
  Let's check:
  
  152293 divided by 37 leaves a remainder of 1.
  
  152293 divided by 67 leaves a remainder of 2.
  
  152293 divided by 97 leaves a remainder of 3.
  
  And 240463=37.67.97, so adding any multiple of this to 152293 will not change those remainders.
• 5 years agoHelpfull: Yes(0) No(0)