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How to prove that $ (\zeta_{p^{n+1}}-1)^{p} $ = $ (\zeta_{p^{n}}-1) $ as ideals where $ \zeta_{n} $ is a primitive nth root of unity ??

How to prove that $ (\zeta_{p^{n+1}}-1)^{p} $ = $ (\zeta_{p^{n}}-1) $ as ideals where $ \zeta_{n} $ is a primitive nth root of unity ??

How to prove that $ (\zeta_{p^{n+1}}-1)^{p} $ = $ (\zeta_{p^{n}}-1) $ as ideals where $ \zeta_{n} $ is a primitive nth root of unity ?

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Suman
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How to prove that $ (\zeta_{p^{n+1}}-1)^{p} $ = $ (\zeta_{p^{n}}-1) $ as ideals where $ \zeta_{n} $ is a primitive nth root of unity ??

How to prove that $ (\zeta_{p^{n+1}}-1)^{p} $ = $ (\zeta_{p^{n}}-1) $ where $ \zeta_{n} $ is a primitive nth root of unity ??

How to prove that $ (\zeta_{p^{n+1}}-1)^{p} $ = $ (\zeta_{p^{n}}-1) $ as ideals where $ \zeta_{n} $ is a primitive nth root of unity ??

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Suman
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Cyclotomic fields

How to prove that $ (\zeta_{p^{n+1}}-1)^{p} $ = $ (\zeta_{p^{n}}-1) $ where $ \zeta_{n} $ is a primitive nth root of unity ??