cmi-entrance 2013 QA5

cmi-entrance · India · pgmath 4 marks Groups Ring and Field Structure

Let $F$ be a field with 256 elements, and $f \in F [ x ]$ a polynomial with all its roots in $F$. Then,
(a) $f \neq x ^ { 15 } - 1$;
(b) $f \neq x ^ { 63 } - 1$;
(c) $f \neq x ^ { 2 } + x + 1$;
(d) if $f$ has no multiple roots, then $f$ is a factor of $x ^ { 256 } - x$.

Let $F$ be a field with 256 elements, and $f \in F [ x ]$ a polynomial with all its roots in $F$. Then,\\
(a) $f \neq x ^ { 15 } - 1$;\\
(b) $f \neq x ^ { 63 } - 1$;\\
(c) $f \neq x ^ { 2 } + x + 1$;\\
(d) if $f$ has no multiple roots, then $f$ is a factor of $x ^ { 256 } - x$.

Paper Questions

QA1 QA10 QA11 QA12 QA13 QA14 QA15 QA2 QA3 QA4 QA5 QA6 QA7 QA8 QA9 QB1 QB10 QB2 QB3 QB4 QB5 QB6 QB7 QB8 QB9