What are the only remainders for any (x squared) divided by 4?

• 0 and 1 are remainders depending on number is even or odd.
  All numbers are 2x or 2x+1.
  
  square of even numbers = 4x^2 which is divisible by 4 . so remainder is zero.
  for odd numbers,
  square of 2x+1 = 4x^2+4x+1 = 4*(x^2+x) +1 .. so remainder is one(1).
• 12 years agoHelpfull: Yes(2) No(1)
• 0 and 1 are the only remainders, for any (x squared) divided by 4.
• 12 years agoHelpfull: Yes(1) No(1)
• Sorry.. ) 0 is the only remainder for any x squared divided by 4
• 12 years agoHelpfull: Yes(0) No(2)
• For x = 1 to 9:
  x |
  1 | {0, 1}
  2 | {1, 0}
  3 | {2, 1}
  4 | {4, 0}
  5 | {6, 1}
  6 | {9, 0}
  7 | {12, 1}
  8 | {16, 0}
  9 | {20, 1}
  Therefore 1 and 0
• 12 years agoHelpfull: Yes(0) No(1)
• All integers are even 2x or odd 2x + 1. If one squares them, we get: 4x^2 and 4x^2 + 4x + 1. This implies that the number is divisible by 4 (evens) or leaves a remainder of 1 (odds).
• 12 years agoHelpfull: Yes(0) No(1)
• Ans. 0 and 1 are the only remainders for any (x squared) divided by 4.
  
  Square of any even is when divided by 4 gives reminder as 0 and square of any odd number when divided by 4 will give reminder as 1.
  
• 12 years agoHelpfull: Yes(0) No(1)