Jan 23, 2011 #1 Aya2002 Advanced Member level 4 Joined Dec 12, 2006 Messages 1,140 Helped 184 Reputation 376 Reaction score 117 Trophy points 1,343 Location Iraq Activity points 8,006 Hello friends, Today I have faced a simple problem. It is the following polynomial of degree 4 (mod 5): g(x) = x + 2x^4 how it will be (3 + 2x^2)(1+x^2)+(2+x) mod 5 ? help please. regards
Hello friends, Today I have faced a simple problem. It is the following polynomial of degree 4 (mod 5): g(x) = x + 2x^4 how it will be (3 + 2x^2)(1+x^2)+(2+x) mod 5 ? help please. regards
Jan 24, 2011 #2 trav1s Full Member level 1 Joined Nov 11, 2010 Messages 98 Helped 29 Reputation 60 Reaction score 28 Trophy points 1,318 Location Japan Activity points 2,025 Just clarification, you are asking to prove that x + 2x^4 = mod5[(3 + 2x^2)(1+x^2)+(2+x)] ?
Jan 24, 2011 #3 Aya2002 Advanced Member level 4 Joined Dec 12, 2006 Messages 1,140 Helped 184 Reputation 376 Reaction score 117 Trophy points 1,343 Location Iraq Activity points 8,006 trav1s said: Just clarification, you are asking to prove that x + 2x^4 = mod5[(3 + 2x^2)(1+x^2)+(2+x)] ? Click to expand... yes friend, this is exactly what I need. Thanks
trav1s said: Just clarification, you are asking to prove that x + 2x^4 = mod5[(3 + 2x^2)(1+x^2)+(2+x)] ? Click to expand... yes friend, this is exactly what I need. Thanks
Jan 24, 2011 #4 A albbg Advanced Member level 4 Joined Nov 7, 2009 Messages 1,312 Helped 448 Reputation 898 Reaction score 409 Trophy points 1,363 Location Italy Activity points 9,999 Developing the polynomial you will obtain: 2*x^4 + 5*x^2 + x + 5 = 2*x^4 + x + 5*(x^2 + 1) rember that sum of moduli is equal to the modulus of the sum, then mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] + mod5[5*(x^2 + 1)] but the last term is always zero since the remainder of 5*(x^2 + 1)/5 is zero then: mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ]
Developing the polynomial you will obtain: 2*x^4 + 5*x^2 + x + 5 = 2*x^4 + x + 5*(x^2 + 1) rember that sum of moduli is equal to the modulus of the sum, then mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] + mod5[5*(x^2 + 1)] but the last term is always zero since the remainder of 5*(x^2 + 1)/5 is zero then: mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ]
Jan 24, 2011 #5 Aya2002 Advanced Member level 4 Joined Dec 12, 2006 Messages 1,140 Helped 184 Reputation 376 Reaction score 117 Trophy points 1,343 Location Iraq Activity points 8,006 albbg said: Developing the polynomial you will obtain: 2*x^4 + 5*x^2 + x + 5 = 2*x^4 + x + 5*(x^2 + 1) rember that sum of moduli is equal to the modulus of the sum, then mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] + mod5[5*(x^2 + 1)] but the last term is always zero since the remainder of 5*(x^2 + 1)/5 is zero then: mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] Click to expand... my friend, I mean how to reduce g(x) to (3 + 2x^2)(1+x^2)+(2+x) mod 5 I know how to develop it, but I need to reduce it to the above equation (mod 5). regards
albbg said: Developing the polynomial you will obtain: 2*x^4 + 5*x^2 + x + 5 = 2*x^4 + x + 5*(x^2 + 1) rember that sum of moduli is equal to the modulus of the sum, then mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] + mod5[5*(x^2 + 1)] but the last term is always zero since the remainder of 5*(x^2 + 1)/5 is zero then: mod5[2*x^4 + x + 5*(x^2 + 1)] = mod5[2*x^4 + x ] Click to expand... my friend, I mean how to reduce g(x) to (3 + 2x^2)(1+x^2)+(2+x) mod 5 I know how to develop it, but I need to reduce it to the above equation (mod 5). regards