P-) 49 the congruence x i(mou p c y solutions. (b) p-1 (a) (d) none of these ) 50. the equation of the fortm a + dy c, where a * 0,b0 and c integcrs, is called

p-) 49 The congruence x I(mou p C y Solutions. (B) p-1 (A) (D) None of these ) 50. The equation of the fortm a + Dy c, where a * 0,b0 and c integcrs, is called a . in two unknowns x and y. (A) Linear diophantine cquation (C) Non-linear diophantinc cquation (D) None of these (B) Quadratic equation 51. The linear diophantine equation ax by= c; a, b, e being integers, has integer solutions if and only if de, where: (A) d g.c.d. of a and (C) d-g.c.d. of a and b and d-(a, b) (D) None of these (B) d-(a, 6) 52. The necessary and sufticicnt condition that a = b(mod m) is: (A) (B) (D) None of these 53. If a=b (mod m) and 0 s 6sthen m is called the : (A) residue of a (mod m) (B) minimal residue ofa (mod mm) (C) maximum residue of a (mod m) (D) None of these 54. The linear congruence ax e b (mod m) is solvable if and only if: (A) dlb (B) d=(a, m) (D) None of these (C) dlb, where d=(a, m) 440)