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The RMD from the inherited IRA would not stop you from making a contribution to your own IRA. The taxes would not be deferred on the RMD by the contribution amount.
With an Inherited Traditional IRA, you’ll pay taxes on any distributions you take this includes an RMD. RMDs cannot be rolled over into other accounts.
If you were to open another IRA then you may be allowed to deduct the contribution amount but that depends on your income and filing status. The deduction may be limited if you or your spouse is covered by a retirement plan at work and your income exceeds certain levels.
The above IRS link shows the limitation based on income.
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